Hebrews quotes the new covenant promise: God will put his laws into minds and write them on hearts, and he will be their God and they will be his people. It also says, “I will be merciful toward their iniquities, and I will remember their sins no more” (Hebrews 8:10–12). These lines are presented as the covenant’s key promises.
In Hebrews 8:10–12, the promise describes what the new covenant will accomplish for the people addressed as “the house of Israel.” God will place his laws inside them, not merely outside them, and will bind himself to them in an enduring relationship: “I will be their God, and they will be my people.” As a result, knowledge of the Lord becomes widespread and. These verses sit inside Hebrews’ argument that Jesus serves as high priest of a better covenant, supported by “better promises” (Hebrews 8:6). Hebrews 8 quotes Jeremiah’s promise of a new covenant (Jer 31) to show what that promised covenant includes and why it differs from what came before.
Hebrews 8:10–12 describes what God promises the new covenant will do. The movement is clear in the text: God acts to place his law inwardly (mind and heart), this creates a stable relationship (“I will be their God…they will be my people”), and it results in a community where knowledge of the Lord is widespread (“from the least to the greatest”).
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with Hebrews 8:10-12, then read the surrounding section so the answer stays connected to the passage's flow.
10"For this is the covenant that I will make with the house of Israel. After those days," says the Lord; "I will put my laws into their mind, I will also write them on their heart. I will be to them a God, And they will be to me a people.
11They will not teach every man his fellow citizen, Every man his brother, saying, `Know the Lord,` For all will know me, From the least of them to the greatest of them.
12For I will be merciful to their unrighteousness. I will remember their sins and lawless deeds no more."