The quote from the Psalm refers to the Exodus. They shall not enter into My rest. St. John Chrysostom above re. They were being tempted to apostasy, to turning away from God, by their Judaic peers, and even Aaron went along with their rebellion. Hebrews is drawing a parallel between the Exodus experience, with which they were all familiar, and their state as Christians on a journey to the promised Kingdom - also in Heb.
Vigilance is needed to keep from drifting or straying into disobedience.
So let us continually, at every hour, renew our bond with God to keep from drifting and straying. True faith and belief in the teachings of Christ implies acceptance of and obedience to His Way and His will. God rested on the seventh day after creating the earth and everything in it. This is still known as the Sabbath in imitation of God. When we fully trust in God, this gives us peace and rest in our souls.