In 1984 Sarajevo hosted the Winter Olympic Games. At the time Sarajevo was part of Yugoslavia, however, since the Bosnian War it has been part of Bosnia and Herzegovina.
Sarajevo has been inhabited since the Neolithic era, (9500 – 4500 BC), but the city of Sarajevo was founded by the Ottomans in 1461, (the exact year is not clear, but 1461 or 1462 seems to be generally used as the year of the founding of the city). The name Sarajevo comes from a contraction of the Turkish words saraj, (meaning court), and ovaši, (meaning field). Apparently there were fields to the west of the government buildings.
So, there you have it, the origin of the name Sarajevo.