Vigils is a term for night prayer in ancient Christianity. See Vespers, Compline, Nocturns, Matins, and Lauds for more information. A Vigil is a night spent in prayer.
A Roman Catholic Mass that counts liturgically for a Sunday or Holy Day but which takes place the previous evening is often mistakenly called a Vigil Mass. But it is more accurately termed an "anticipated Mass," because a Vigil is actually the whole day prior to certain major feasts, which acts as sort of Western version of the forefeast. And such Vigils (such as Christmas Eve) have their own proper Mass theoretically said that morning.