Eileen is an Anglicised form of the older Irish Gaelic names Eilin and Aibhilin. (Such names were often Anglicised with an "een" ending.) Both these derive from Norman French, and are probably versions of Ava or Aveline. Ava itself is of Germanic origin and uncertain meaning. There was a St Ava in France in the 9th century, but the name was rarely used until the 20th, when the fame of Hollywood actress Ava Gardner made it a popular choice for girls.
Eileen was better known in Ireland than anywhere else until the early 20th century, when it became popular all over the English-speaking world. It was especially well known in the 1980s when Dexy's Midnight Runners produced their hit song "Come on Eileen."
There is a less widespread Scottish variant, Aileen, and there is no masculine .EQUIV.alent.