Do not confuse Capitol (with an ‘o’ as the penultimate letter) and capital (with an ‘a’ as the penultimate letter). Although the two words have the same etymology – both come from the Latin caput, genitive capitis, ‘head’ - and are pronounced in the same way (IPA: /'kæ pɪ təl/), they have quite different uses.
For the various meanings of capital - by far the more common of the two words - see Capital.
The Capitol – always in this use with the definite article and with an upper-case initial letter – is the English form of the name of one of the seven hills of ancient Rome. Its name in Latin is Capitolium, and it is also referred to in English as the Capitoline Hill (in Latin mons Capitolinus). The Capitol had two peaks: on its northern peak there was a citadel, and on its southern peak a temple to the Roman god Jupiter and the goddesses Minerva and Juno. This temple is sometimes also referred to as the Capitol. In Roman times the inhabitants of many cities in Italy and in the western provinces of the Roman Empire imitated the Capitol in Rome by building a temple to Jupiter on a hill within their city and referring either to the hill or to the temple or to both as the Capitol.
In modern times the Capitol is the name of the building which houses the United States Congress in Washington D.C. The neo-classical building, which was completed in 1800, is situated on Capitol Hill (formerly Jenkins’ Hill); its north wing houses the Senate, and its south wing the House of Representative. The building’s name was chosen by Thomas Jefferson (1743-1826), one of the Founding Fathers of the United States, principal author of the Declaration of Independence, and third President (1801-1809), who insisted on this name rather than ‘Congress House’, the name originally proposed. In the United States capitol, sometimes with a lower-case initial letter, may also be used with the same meaning as ‘statehouse’, to refer to any building which houses a state legislature: the Utah capitol, e.g., is the building which houses the legislature of the state of Utah.