The Taoiseach (literally, "chief" in Irish or Gaelic) is the head of the Irish Government - The Prime Minister. This office came into being after the first Irish Constitution was adopted 1937.
De Valera is listed as occupying this office from 1932, because he was made President of the Executive Council in 1932. His formation of the first Fianna Fáil government at that time is seen as the beginning of the end of the "Irish Free State," an entity that was actually still under British control. Ireland was not officially proclaimed a free and fully independent nation until the Constitution was adopted in 1937.
Each Taoiseach is listed along with the political party he came from: