Bohemia is the Latin name of the territory inhabited by Czechs. It is one of two main regions in Czech Republic. The other one is Moravia.
The Bohemians (i.e., Czechs) and the Moravians have lived in one country for centuries as Kingdom of Bohemia and Moravia. It later became part of the Austrian Empire which later yet became the Austro-Hungarian Empire. This was made possible after the same person became both the Emperror of Austria and King of Bohemia and Moravia.
After the fall of Austro-Hungarian Empire the representatives of Bohemia and Moravia met with representatives of Slovakia in the Moose lodge, near Stanley Theatre, in Pittsburgh, PA, and decided to join forces as one country called Czechoslovakia. This is known as Treaty of Pittsburgh. (By the way the Moose building was torn down in the late 1980's or very early 1990's, I do not remember the exact year, but I do remember people complaining that the only building in town in which a country was created was about to be torn down, and that Americans have no appreciation for history.)
Anyway, the marriage between Czechs and Slovaks ended up in divorce in 1938, about six months before the start of World War II when Slovak National Council declared independence. Subsequently, Nazi Germany annexed both Bohemia and Moravia, called it Protectorate of Bohemia and Moravia and made it part of the Third Reich. Of course, the name Protectorate meant protecting the interests of the Nazi, not of the Czechs and Moravians. In 1942, with the help of exiled Slovak soldiers the Czechs (assisted by the British) assassinated Reinhard Heydrich, the Nazi "Protector" which led to a real bloodbath.
At the end of World War II (1945) Czechoslovakia was re-established, this time not by a mutual treaty, but by the Allies. Again, it was not a happy marriage.
In 1967 Slovak Communist leader Vasil Bilak exchanged some really angry words with Anonin Novotny the then President of Czechoslovakia and chairman of Communist Party of Czechoslovakia. This led to a mutual agreement in 1968 which turned Czechoslovakia into a federation, in which the Czechs and Moravians had their own government, and Slovaks had theirs. Only things like the Army and police and a few others were governed on the federal level.
The invasion of Czechoslovakia by Soviet Union and other Communist countries on August 21, 1968 truly united the Czechs and Slovaks who formed friendship not heard of before. I was 18 at the time, and my generation was not much into ethnic antagonism. I guess we were the second generation of children of Czechoslovakia and we were not too interested in fighting each other.
Nevertheless, in 1993, four years after the fall of Communism, Czechoslovakia had a referendum in which both, the Czechs (with the Moravians) and Slovaks agreed to remain friends but as separate countries. This made sense because despite many similarities, the two cultures are quite distinct.
The Latin name of the Czech region comes from an ancient tribe of the Boiohemi which no longer exists. The name stuck because by the time the Czechs came in Latin was a rather dead language (somewhere around the 6th or 7th Century, I am not exactly sure). However, the Czechs call Bohemia Cechy (with a caron above the initial 'C'), and Moravia Morava.
For whatever reason, the English language uses the Latin name. I often get asked why the Czech territory is called Bohemia and not Czechia (or something similar). To that I usually reply, "Beats me, I did not invent the English language." That usually makes people realize the practice of calling Czechia Bohemia is an anachronism of the English language, not of the Czech people who do not call their home Bohemia, nor themselves Bohemians.