The Czech Republic´s existence is only 25 years long and there is not anything special or substantial contribution to the world in the period between 1993 and today in my opinion.
But, Czechia´s - thus, the country in whole (both in contemporary and historical context) heritage is rich. What is the biggest one cannot judge. Everybody can choose :-)
1. Music - throughout more than one thousand years old history of Czechia - can be considered beneficial in both European and worldwide context, several times co-determined or determined a newly arriving era in musical art, above all in music of Classical era (Jan Václav Stamic, Jan K.Vaňhal, Josef Mysliveček, Antonín Rejcha), as well as by original attitudes in Baroque (Adam Michna, Jan Dismas Zelenka), Romantic era (Czech national music - Czech music school): Bedřich Smetana, in late Romanticism the greatest Czech composer Antonín Dvořák - among other things, the founder of American classical music and in Czechia born Gustav Mahler), and modern classical music (inimitable composer Leoš Janáček and Bohuslav Martinů), discovery in microtonal music (Alois Hába), high modern era (Miloslav Kabeláč, Petr Eben). More in my article: Czechia the heart of Europe | Music
2. Arts - in general, the Czech art is known worldwide for its individually made, mouth blown and decorated art glass and cut crystal, garnet and other gems jewelry, decorative and applied art. Painting: works of the Gothic era - Master of Vyšší Brod altar, the founder of the style, which dominated European painting around 1400. Baroque - An exceptional Czech artist Václav Hollar, the etcher of worldwide recognition. Art Nouveau and modernism - Alfons Mucha, world famous and one of the best known Czech artists. Abstract painting - František Kupka: a pioneer of abstract art, influencing substantially all modern painting movements. Interesting personalities in expressionism, cubism, and Cubo-expressionism, original post-war symbolism (Mikuláš Medek) and “explosionism” movement (Vladimír Boudník). Film and theatre: Karel Zeman, a pioneer with special effects (culminating in successful films such as artistically exceptional "Vynález zkázy" (A Deadly Invention, 1958); so-called Czech New Wave of the 1960s (linked with names of Miloš Forman, Věra Chytilová, Jiří Menzel, Ján Kadár, Elmar Klos, Evald Schorm, Vojtěch Jasný, Juraj Herz, etc.) and director František Vláčil with the original manuscript and the deep psychological impact with the extraordinary high-quality art received international acclaim; Jan Švankmajer - a filmmaker, known for his animations and features, which greatly influenced artists worldwide. Original Czech cultural phenomenon came into being at the end of the 1950s. This project called Laterna magika (The Magic Lantern) considered the first multimedia art project in international context.
3. Literature - Comenius (philosopher and writer), the innovator who first introduced pictorial textbooks, F.Kafka - widely regarded as one of the major figures of 20th-century literature, humorist J.Hašek (The Good Soldier Švejk - the book which was translated into 60 languages). Names as B.Hrabal, K.Čapek and M.Kundera cannot be forgotten. Poetism - Czech literary avant-garde style and movement in poetry (main representant Jaroslav Seifert, Nobel Prize holder).
4. Architecture - Czechia is the country with rich architectural heritage from the Romanesque period until modern times, being the place of origin of several unique styles - unique mixture of Romanesque and Gothic style represents St. Procopius Basilica in Třebíč, considered to be the most bizarre work of the European architecture of the 13th century, Czech Baroque due to its complexity and uniqueness became an independent concept art history, an architectural singleton is the Baroque Gothic style (Jan Blažej Santini), a specifically Czech architectural style, called ‘Rondo-Cubism’, came into existence after 1918. Together with the pre-war Czech Cubist architecture, it is unparalleled elsewhere in the world. There are also contemporary Czech architects whose works can be found all over the world, e.g. works of Jan Kaplický.
5. Science - Prokop Diviš: lightning rod inventor; Jan Evangelista Purkyně: anatomist and physiologist of the first half of 19th century, discoverer of Purkinje cells in the brain (1837), was the first to use a microtome to make wafer thin slices of tissue for microscopic examination. He is also known for his discovery in 1839 of Purkinje fibers, the fibrous tissue that conducts electrical impulses from the atrioventricular node to all parts of the ventricles of the heart. Other discoveries include Purkinje images, reflections of objects from structures of the eye, and the Purkinje shift, the change in the brightness of red and blue colors as light intensity decreases gradually at dusk. Purkyně also introduced the scientific terms plasma and protoplasm the substance found inside cells. He was one of the best-known scientists of his time. Josef Ressel: ships propeller inventor. Gregor Mendel: the founder of the modern science of genetics, in Czechia born and working; Bedřich Hrozný - orientalist and linguist who deciphered the ancient Hittite language and laid the groundwork for the development of Hittitology. Sigmund Freud, neurologist and the founder of psychoanalysis; Jaroslav Heyrovský: the inventor of the polarographic method, father of the electroanalytical method. Otto Wichterle - inventor of soft contact lenses. Stanislav Grof: founder in the field of transpersonal psychology; Antonín Holý - chemist of world recognition, inventor of the most effective drugs in the fight against the AIDS epidemic.
6. Statesmen and influential personalities - St.Adalbert of Prague (in Czech svatý Vojtěch): Czech priest, bishop of Prague, who brought Christianity to nations of Central Europe - Hungarians, Poles, and Prussians. Přemysl Otakar II: Czech king, ruler of seven other countries, his reign stretched from Silesia to the Adriatic coast, founder of many towns and cities not only in Czechia, but in contemporary Poland and Prussia (13th century). Charles IV: Holy Roman Emperor. probably the most famous personality of the Czech state ever. He rebuilt the city of Prague as the capital of Central Europe and one of the intellectual and cultural centers of Europe. In 1348, he founded the Charles University in Prague, which was named after him and was the first university in Central Europe and third in Europe. Jan Hus - theologian, a Catholic priest, philosopher, who became a church reformer, an inspirer of Hussitism, a key predecessor to Protestantism and a seminal figure in the Czech Reformation (14–15th cent). King George of Poděbrady (Jiří z Poděbrad) - well known for his idea and attempt to establish common European institutions and supranational insignia. It is seen as the first historical vision of a European unity forgoing the European Union (15th century). Above mentioned Comenius (Jan Ámos Komenský) - inventor in educational systems, the theory of education, practical educational work, methods of education (17th cent.); Tomáš Garrigue Masaryk - the main personality of the founding of free modern Czech (and Slovak) democratic state in 1918
7. Soldiers - Jan Žižka: controversial Czech general, a contemporary and follower of Jan Hus, successful Hussite military leader (died 1424). He is considered to be among the greatest military leaders and innovators of all time. His accomplishments in this regard are especially unique and noteworthy as he had to quickly train peasants to repeatedly face highly trained and armored opponents who usually severely outnumbered his own troops, and for this, some have considered him to be the greatest general in history. Žižka developed tactics of using wagon forts, called vozová hradba in Czech (wagons fortification) as mobile fortifications, predecessors of tanks, with an original multifunctional armament of soldiers; Josef Václav Radecký (known internationally as Joseph Radetzky von Radetz): Czech nobleman and field marshal, chief of Austrian army (Czech lands were at that time a part of Austrian empire) who is considered one of the best commanders of 19th-century Europe. During his military career, he actively participated in the defeat of Napoleonic France and the reform of the army. Josef František - fighter pilot of World War II, the highest-scoring Allied ace in the Battle of Britain (1940)
8. products - Czech beer, worldwide known product of Pilsener (Plzeň/Pilsen - the city in the western part of Czechia) types of beers brewed by original technology using Czech raw materials (Bohemian hop); Bohemian glass - glass products made by original technologies, cutting-edge design and inimitable craftsmanship (incl.co-called Bohemian crystal - hand cut glass products). porcelain and jewelry, using own raw-materials, e.g.Bohemian garnet in the jewelry; Tamara and Věra radar system (passive sensor) of third generation, able to recognize targets of “stealth” type; Semtex worldwide known explosives; some original products of the Czech cuisine - above all pastries (salty and sweet as “koláče” & “buchty”), Czech finger sandwiches, Prague ham: a type of brine-cured, stewed, and mildly beechwood-smoked pork boneless ham, Shpikachki (špekáčky) - type of sausage, made from finely cured mixture of pork and beef with smoked bacon liner, Bohemian breaded dumplings, pickled sausages (called “utopenci”, which means “drowned”) and fishes (“zavináče”), cheeses and vegetables (well known Znojmo pickled cucumbers), beer cheese, ripened cheeses (well known “Olomoucké tvarůžky” etc.), Czech potato pancakes, etc.; liquors - Wallachian “Slivovice”: strong plum brandy and “Becherovka”: sweet herbal liqueur from Karlovy Vary.
9. Czech words, which became international - robot (invented by Karel Čapek in his stage-play R.U.R., derived from the word “robota”, which was a compulsory unpaid work for landowners in the past), pistol (from Czech word “píšťala”), houfnice (English “howitzer”), polka, dollar (from Czech word “tolar”), hocus-pocus, tunel (in the sense of “tunnel the bank” - to rob the bank's assets by transferring money elsewhere by its own owners)
10. Sportsmen - football: Josef Bican, the greatest goalscorer of football history in Europe (and probably in whole world), Emil Zátopek - long-distance runner, only person to win the 5,000 metres, 10,000 metres, and marathon in the same Olympics, Věra Čáslavská - seven Olympic gold medals holder in gymnastics, all in individual events, which is an all-time record among female Olympians, Martina Navrátilová - tennis player, arguably the best female tennis player of all time, multiple winner of women's singles title at Wimbledon, Jaromír Jágr - ice hockey player, the best European player in the history of Canadian-American National Hockey League, ranking overall 2nd in points, third in goal scores, and first in the number of game-winning goals in all history of NHL.
(I hope that the other great personalities of Czechia I did not mention will forgive me) :-)
Vladimír Hirsch (Quora, 2018)