The concluding argument is made in chapter 10 that Jesus is the final offering, once and for all, for the sins of the people and that this offering is infinitely better than the blood of lambs and bulls. The offering of Jesus is the sign of the new covenant (16-18) that is now established internally and eternally.
Because of this we must persevere. The author says we "have confidence (19)" that Jesus has "opened a way through the curtain (20)" and now that we have a "great priest over the house of God (21)" we can approach with full assurance having been washed clean. We must hold fast to what we believe. Remember the context of the letter is that people were NOT holding fast and were leaving the faith to return to their former practices.
I especially like verse 24 -- let us provoke one another to love and good deeds. What a great concept. Instead of provoking others to violent responses or other behaviors the goal of the church is to help us provoke one another to do more good. The key to this is "not neglecting to meet together (25)." Christianity knows no religion but social religion -- that is to say we are called to live life in radical community with one another. A community that challenges and encourages; a community that teaches, trains and deploys. Without the community of faith it is not possible to live the life Jesus called us to live. This is, perhaps, the greatest challenge for the modern church. The challenge of creating (and recreating) authentic Christian community where we lift, challenge, and "provoke" one another to live the life we are called to live.