The author spends a lot of time discussing agreements between God and mankind. One was made through Moses and the other through Jesus. You can probably guess which one is greater.
PRIESTS & SACRIFICES
Priests show up all over Hebrews: Aaron and his sons, Melchizedek, and Jesus. He also brings up the sacrifices those priests made, the nature of their offices, and the like.
OLD TESTAMENT HEROES
Hebrews gives many, many nods to the characters of the Old Testament, and not all of them are the ones you heard about in Sunday school.
JESUS IS GREATER
Jesus is greater than those heroes. The author brings this up time and time again. Because of who he is and what he did, Jesus surpasses everything and everyone else.
WARNINGS AGAINST GIVING UP
The readers were coming under fire for their faith (12:4), but the author encourages them to “hold fast” to their confession of Jesus.