The literal meaning of Sabbath is to rest from work. Typically we think of that rest occurring on a weekly basis.
In the Old Testament of the Bible, that rest occurred on the seventh day (which equates to Saturday on the modern calendar). This was exemplified in the creation account (Genesis 2:2) when God rested on the seventh day. Later, it was reiterated to Moses (Exodus 16:23 and Exodus 20:11).
For most Christians, the Sabbath day of rest is on the first day of the week, or Sunday. This change of day is seen implicitly through Jesus, who is “Lord of the Sabbath” (Luke 6:5), when he rose from the dead (Luke 24:6) and later when he appeared to his followers (Luke 24), both on the first day of the week. Pentecost (Acts 2:1), when the Holy Spirit was given, also occurred on the first day of the week.
In the Old Testament, there are also Sabbaths prescribed at various times for different lengths, although the typical usage refers to one day each week.