Douglas Wilson has some excellent exegetical comments on Heb. 3:1-6 over on his blog, Blog and Mablog. Below are some excerpts.
The phrase “apostle and high priest” is striking. This is the one place in Scripture where Christ is called an apostle, that is, one who is sent out. A “sent one” has the authority and commission of the one sending. For example, an apostle of a church is one like a missionary or church planter. And apostle of Christ is sent out by Christ and has His authority, as did the Twelve. In this instance, Christ is described as an apostle. He was sent out by God the Father, and represents God to us. At the same time, He is described as a High Priest””that is, as one of us to represent us to God. A priest is chosen from among the people and stands before them to represent them. This phrase “apostle and high priest” therefore means that Christ is the perfect bridge between God and man. As an apostle of God, He represents God perfectly to us, and as our High Priest, He represents us perfectly to God….
We are that house. The Bible is very clear that we are God’s building, God’s house….
Given this, what is necessary? We must hold firm to the end. We see here, stated plainly, the doctrine of perseverance. Whose house we are, if . . . Three classes of men exist. Some are never in the house. They have no connection to the Christian faith at all. Some are in the house, but only temporarily. They are covenantally connected to Christ, and the connection is a real one, but they are not elect. The true sons of the house, however, the elect of God, abide there forever. “And a slave does not abide in the house forever, but a son abides forever. Then if the Son makes you free, you shall be free indeed” (John 8: 35-36). [Read the whole post.]
∼striving for the unity of the faith for the glory of God∼ Eph. 4:3,13 “¢ Rom. 15:5-7