A repeated theme of Hebrews so far has been "holding on to hope and confidence in Yahweh so that we can be engaged in his plans and experience his blessing and rest". In these verses, the author gives us an example of someone who did this well, and also builds a case for trusting in Yahweh based on his character and being.
Some people might be uncomfortable with the idea of a God who desires praise and worship. This might seem egotistical to some. But driving one day in college I stopped briefly on some "radio preacher" who defended God's desire for praise in an interesting way. He essentially said, "God looked around for something better and didn't find anything!" God objectively knows he is the greatest being in existence. He knows there is nothing more good, fascinating or exciting to obsess over, yet out of love he wants everyone to experience the best that there is. Since he IS the best that there is, it only makes sense that he would desire all of creation to enjoy and obsess over him!
In a similar way, when Yahweh vowed to bless and multiply Abraham, he swore by his own name, reputation and character, since there was no one greater to swear by. This tells us something about Yahweh. He is not one option among many. He is not equal to other gods or ideas of "the ultimate". He is the greatest. He does not, like polytheistic gods of other religions, have anyone else to even potentially compete or argue with. We do not place our fate in the hands of a god who might someday be overruled by another god. We place our fate in the hands of the greatest and the best. And this is the implied reason that Yahweh is worthy of Abraham's trust and our own.
The author points out that when someone swears by something greater or more valuable than themselves ("I swear to God", "on my mother's life", etc.) we take them seriously and usually assume that what they are saying or promising is trustworthy, provided their character is not suspect. Yet this trust isn't foolproof, because people are still people and might be lying.
By contrast, when God swears an oath, appealing to his own reputation and character, we can trust him far more, since he is the greatest thing one could appeal to in a vow, and he is also incapable of deception! The point the author is making is that we have every reason to be confident and trust in Yahweh.
In our fiction and in our own minds, even in scripture, God is described in human terms ("Father", "Shepherd", etc.). But these are just limited metaphors that are only useful to a point. The problem we run into is that we imagine God to be too much like us, perhaps in an effort to mentally relate to him more easily. But when we do this, we end up with a god that might give up on us if he becomes impatient enough. Or a God who is flawed and worth rebelling against. (Look no further than the movie "Legion" or TV shows like "Supernatural" and "Dominion" for examples of this kind of thinking.)
Ironically, having a right understanding and trust in God is where we geeks may actually have an advantage! Picturing Yahweh correctly requires some "out of the box" thinking. Yahweh is NOT like us. He is not flawed in any way. If we have trouble trusting him because we've been burned by people, we should remember to mentally place God in his own category entirely.
That's what Abraham did. He trusted in Yahweh's promise to give him a child and descendants, even though he had to wait for that promise to be fulfilled for 25 years! But he waited and trusted because he knew the truth: More than anyone else and without any limitations, Yahweh is worthy of our trust, our commitment, and our hope for eternity.