This is the seventh post in a series from Hebrews 11. You'll find all the posts done so far in this series listed here.
The verses in Hebrews 11 that come right before the section we look at in this post are about Abraham's faith, and the verses right after it are about Abraham's faith as well, but in this section, the writer takes a little time out to summarize what's been said so far.
These all died in faith without receiving the things promised, but they saw them in the distance and welcomed them and acknowledged that they were strangers and foreigners on the earth. For those who speak in such a way make it clear that they are seeking a homeland. In fact, if they had been thinking of the land that they had left, they would have had opportunity to return. But as it is, they aspire to a better land, that is, a heavenly one. Therefore, God is not ashamed to be called their God, for he has prepared a city for them. (Hebrews 11:13-16 NET)
"These all", of course, is all the "people of old" discussed in the chapter so far. Common to all these people of faith is that when they died, they had not yet received the things promised to them. They had received a partial fulfillment of God's promises, but there were things God had promised them that were yet to come when they died.
Take Abraham as an example. In chapter 6 of Hebrews it tells us that because Abraham persevered, he "obtained what was promised." Having a son was a fulfillment of God's promise to Abraham, but it was just the first step in the promise that God would make him "into a great nation." I'm sure that Isaac's miraculous conception and birth strengthened Abraham's faith in the rest of God's promise, but the biggest part of God's promise--that God would make a great nation of him and that all the families of the earth would be blessed through him--had not yet come and was obviously very far off in the future when Abraham died.
It would have been the same with all the people listed in this chapter. They'd seen enough of God's work to know that he would do as he'd said, but much of what God had promised them remained uncompleted when they died. They died in faith, still convinced of things they did not see.
Furthermore, the communion they had with the God who had promised them these things caused them to see themselves as foreigners on the earth. They never quite belonged in their worldly surroundings because they longed for something more: a better land, that is, a heavenly one. Their longing wasn't for an earthly place; it was a longing to be with God. The writer tells us that they could have returned to the land they'd left, if an earthly place to belong to was what they wanted, but that wasn't it. They sought God, and because he's what they wanted, they aspired to a heavenly land.
As a result of this sort of trust in God's faithfulness to fulfill his promises, and their continued longing to be with God above anything else, "God is not ashamed to be called their God." What a statement that is! God called himself "the God of Abraham, Isaac and Jacob", and yet, when read these men's stories, we can see that they were not perfect men, and were not always men of the strongest faith, but because they sought God and believed he would fulfill his promises to them God identifies himself with them.
And the heavenly land they longed for? It's already built.
But you have come to Mount Zion, the city of the living God, the heavenly Jerusalem, and to myriads of angels, to the assembly and congregation of the firstborn, who are enrolled in heaven, and to God, the judge of all, and to the spirits of the righteous, who have been made perfect, and to Jesus, the mediator of a new covenant, and to the sprinkled blood that speaks of something better than Abel's does. (Hebrews 12: 22-24 NET)
It has come through Christ. Jesus is the mediator of the new covenant and his blood brings people right into the presence of God (Hebrews 10:19). That's the purpose of the whole gospel story: Jesus died to "bring us to God (1 Peter 3:18)."
When God promised Abraham that through him all the families would be blessed, it's this that he's referring to: Jew and Gentile would both be reconciled to God through the cross. What these faithful "people of old" longed for most--the heavenly country where people can be in the presence of God--had not yet come, but God was bringing it about through them, and they died in faith, trusting that he would fulfill his promises to them.