Sunday is the Lord's Day. Christians consider it the sabbath in contrast to their Jewish forebears who celebrated Saturday as the day of rest. Christians altered the celebration due to St. Peter's recognition that we are children of the eighth day. There are some traces of this in modern languages such as Spanish which still call Saturday by the name sabbath - Sabado.
In continuity with Jewish tradition, though, liturgical churches such as the Roman Catholic church sometimes treat the evening before as the beginning of the following feast day. Jews, for example, start their sabbath celebrations on Friday evening. This practice goes back to the first chapter of Genesis: Evening and morning followed, the first day, etc.
The same goes for Sunday liturgical celebrations. We begin with First Vespers on Saturday evening, with the readings already preparing us for the subjects of the next day's readings.