Charles Ellicott Commentary Exodus 31:13

"Speak thou also unto the children of Israel, saying, Verily ye shall keep my sabbaths: for it is a sign between me and you throughout your generations; that ye may know that I am Jehovah who sanctifieth you." — Exodus 31:13 (ASV)

It is a sign between me and you.—Circumcision had been given as a covenant sign to Abraham and his descendants (Genesis 17:9–13); but its adoption by many of the Gentile nations had rendered it no longer a distinguishing mark by which God’s people could be certainly known from others.

Thus, a new sign was needed. The observance of one day in seven as a day of holy rest became from then on the distinguishing sign, and proved effectual. It was not likely to be adopted, and in point of fact was not adopted, by any of the Gentiles. We find it in the latest time of the Jewish nation still regarded as the special mark and badge of a Jew (Juv. Sat. vi. 159, 14:96; Mart. Epig. 4:4, 50:7, etc.).