God wants to give you access to his very presence, to his very throne. He wants you to be able to come to him. The way was closed until Jesus Christ came and died to open it up:
Therefore, brothers, since we have confidence to enter the Most Holy Place by the blood of Jesus, by a new and living way opened for us through the curtain, that is, his body Heb 10:19-20
And he lives and presides as Great High Priest to keep it opened up:
and since we have a great priest over the house of God Heb 10:21
The words that hit me are the "us" and the "we". This is for me! This is for every Christian. This is available to anyone who isn't a Christian yet if they put their trust in Jesus Christ. He has done this for you, he offers this to you, why on earth wouldn't you come??
The writer has four consequences for us, four "let-us"es:
1. Let us draw near to God with a sincere heart in full assurance of faith having our hearts sprinkled to cleanse us from a guilty conscience and our bodies washed with pure water v22. Assurance is full because guilty conscience has been cleansed. (I won't labour the point that the baptism reference is linked to what happens when our consciences are cleansed by trusting Jesus)
2. Let us hold unswervingly to the hope we profess because he who promised is faithful v23. Note that the reason to hold unswervingly isn't us, it is the one who promised. I am fickle, he is sure. I might give up, he is never going to. I am confident not because of me but because of him
3&4. Let us consider how to spur one another on to love and good deeds and let us not give up meeting together. Both of which are about encouraging each other to hold unswervingly to Jesus as we anticipate his day coming. Holding unswervingly is something we do together. If you are reading this as someone who says "I am a Christian but I don't have to be part of a local church of Jesus Christ" Hebrews says you are wrong.
Note too that people who come to the throne of God, receiving grace and acceptance there, spur one another on to love and good deeds. This is the purpose of church meetings. They are not a social club, they are not a lecture, they are not individualised worship times. It is not appropriate to have bad relationships there, it is wrong to "come for what I get". We are there as the local company of those who draw near to God, to encourage each other in love and good deeds for God's glory. If your fellowship isn't loving and isn't encouraging each other in the good deeds, maybe you haven't drawn near to God like you should.