Thus the heavens and the earth, and all the host of them, were finished. And on the seventh day God ended His work which He had done, and He rested on the seventh day from all His work which He had done. Then God blessed the seventh day and sanctified it, because in it He rested from all His work which God had created and made.
As Exodus 20:11 reiterates, the Sabbath is a memorial of Creation, particularly the seventh day of that week, in which God rested as an example to mankind. God used the first six days of Creation Week to complete His labors, and on the seventh day, He rested, blessing and hallowing that time for a different kind of pursuit. Therefore, God commands mankind to observe the day similarly—by ceasing from our labors and resting.
Obviously, Genesis 2:1-3 does not contain the word "Sabbath." However, it certainly emphasizes "the seventh day," mentioning it three times, and the Hebrew verb shabath ("rested") appears twice. This combination strongly indicates that the seventh-day Sabbath is a day of rest.
The author of Hebrews, traditionally the apostle Paul, makes this connection in a New Testament setting in Hebrews 4:4, 7-9:
For He has somewhere spoken of the seventh day in this way: "And God rested on the seventh day from all His works" [Genesis 2:3]. . . . [A]gain He appoints a certain day, "Today," saying through David so long afterward, in the words already quoted: "Today, if you will hear His voice, do not harden your hearts" [Psalm 95:7-8]. For if Joshua had given them rest, God would not have spoken of another day later on. So then, there remains a Sabbath rest for the people of God. (English Standard Version)
The plain sense of Paul's argument is that New Testament Christians keep the seventh-day Sabbath because—among other reasons—God's rest has not been fulfilled in His plan. The Sabbath teaches us a great deal about what God is doing and what is our part in it. God sanctified, or set apart, the Sabbath as a day of rest for our benefit, that is, so we can learn and grow spiritually.