“Moreover also I gave them my sabbaths to be a sign between me and them that they might know that I am Yahweh who sanctifies them.”
The importance of the sabbath as a sign that Israel were God's people is stressed here. The keeping of the sabbath, first mentioned in Exodus 16 and ratified in Exodus 20, demonstrated that they were a people ‘set apart' (sanctified) by Yahweh for Himself, and looked on as His own people. See on this Exodus 31:13-17. The Sabbath had a dual purpose for the Israelites. It was a constant reminder to them that Yahweh was the great Creator of all things (Exodus 20:11), and it reminded them of His creation of their nation (Deuteronomy 5:14-15). It was the central sign of the Old Covenant (Isaiah 56:2; Isaiah 56:4).
Paul too indicated that to keep a day (or all days) to the Lord was right, but stressed that the particular day was unimportant. What mattered was the keeping of one day for Him (Romans 14:5-6). However in contrast with the Jewish Sabbath the early church generally did not see it as a day of total rest, but as a day for serving God.