What does Hebrews 6:17 mean?

Oaths are what insecure, fallible human beings expect from sinful, fallible human beings in order to have confidence in a promise. There is a natural human tendency to be suspicious of another person's word. Oaths are meant to add an extra layer of reassurance that we're telling the truth. Of course, if a person is fundamentally honest, then there's no purpose to such a vow, other than to make the other person feel better.

This is exactly why God chooses, at times, to use the concept of an oath when dealing with humanity. As the prior verse indicated, human oath-makers have to swear on something greater than themselves. In God's case, there can be nothing higher to swear on, other than Himself. And, as the next verse will show, the facts of history and the nature of God provide two infallible proofs that His oaths are always reliable.

The context of this theme is confidence leading to obedience, maturity, and growth. When we're persecuted, we might doubt God, and lack the drive to grow in our faith. This, in turn, makes us all the more vulnerable to attacks, and more likely to "fall away." Instead, we should recognize the absolute reliability of God's promises, and seek to grow in both truth and love. The ultimate expression of this promise, and the best reason for our hopeful confidence, is the "anchor" of Jesus Christ.

According to the Bible, all believers are spiritual heirs of the promises made to Abraham (Galatians 3:29). While we are not all physical heirs, or part of the literal nation of Israel, we are part of the promises God made to that patriarch.