The Greek word translated “better” in the book of Hebrews is used 19 times in the New Testament. Thirteen of those uses are found in Hebrews. One recurring theme in Hebrews is that Christ has brought in a better covenant. Thus the word “better” dominates the book, especially from chapter six on. I wanted to list all the places “better” is used in Hebrews. These verses are not hard to understand, but at the end I will explain briefly what it all means. These verses are from the English Standard Version translation.
(Heb 1:4) Having become as much superior to angels as the name he has inherited is more excellent than theirs.
(Heb 6:9) Though we speak in this way, yet in your case, beloved, we feel sure of better things—things that belong to salvation.
(Heb 7:19) (for the law made nothing perfect); but on the other hand, a better hope is introduced, through which we draw near to God.
(Heb 7:22) This makes Jesus the guarantor of a better covenant.
(Heb 8:6) But as it is, Christ has obtained a ministry that is as much more excellent than the old as the covenant he mediates is better, since it is enacted on better promises.
(Heb 9:23) Thus it was necessary for the copies of the heavenly things to be purified with these rites, but the heavenly things themselves with better sacrificesthan these.
(Heb 10:34) For you had compassion on those in prison, and you joyfully accepted the plundering of your property, since you knew that you yourselves had a better possession and an abiding one.
(Heb 11:16) But as it is, they desire a better country, that is, a heavenly one. Therefore God is not ashamed to be called their God, for he has prepared for them a city.
(Heb 11:35) Women received back their dead by resurrection. Some were tortured, refusing to accept release, so that they obtain a better resurrection.
(Heb 11:40) Since God had provided something better for us, that apart from us they should not be made perfect.
(Heb 12:24) And to Jesus, the mediator of a new covenant, and to the sprinkled blood that speaks a better word than the blood of Abel.
Here are the points in condensed form.
First, Jesus has a better name, introduces a better hope, is the mediator and guarantor of a better covenant that is enacted on better promises and has offered a better sacrifice that speaks a better word than Abel.
Second, the Old Testament saints looked forward to a better country and a better resurrection.
Finally, the readers of the book of Hebrews are expected to press forward to better things, to give up their possessions because they had a better possession, and they are made better by being joined with the Old Testament saints.