Notice which day is "the Lord's Day." God calls the Sabbaths "My Sabbaths." The Sabbaths, weekly and annual, are His; they do not belong to us, nor are they "Jewish Sabbaths" or "Gentile Sabbaths." The Sabbath is a space of time. That time, whenever it arrives, is not ours but God's. If we appropriate it for our own use, whether for work or pleasure, we are stealing that time from God! In Exodus 20:8, He commands us to "keep it holy." God made it holy time, and commands us to keep it holy rather than profane it.
"Surely My Sabbaths you shall keep, for it is a sign between Me and you throughout your generations, that you may know that I am the Lord who sanctifies you" (Exodus 31:13). Here, then, is the purpose of the Sabbath: ". . . it is a sign." A sign is a badge, symbol, mark, or token of identity. Webster's Dictionary defines a sign as "a display used to identify or advertise a place of business or a product. Something indicating the presence or existence of something else."
The word Moses wrote in Hebrew is 'owth, which means "a sign, signal, distinguishing mark, banner, remembrance, warning; a token, ensign, standard, miracle, proof" (Brown, Driver & Briggs Hebrew Lexicon). A banner or flag identifies a nation or group. A signal like a beacon announces the existence of something, like a rocky shore, that others need to be warned about. A token is a visible sign that serves to make something known, such as a white flag is a token of surrender.
God commands His people to keep His Sabbaths as a sign. It is a sign between God's people and God: "It is a sign between Me and you." It is a badge or token of identity, advertising, announcing, or proclaiming certain identifying knowledge: ". . . that you may know that I am the Lord who sanctifies you."
The Sabbath is the sign that identifies to people who their God is. It is the sign by which we may know that He is the Lord. It identifies God, and by so doing, it identifies who His people are as well.