God causes us to "come near"; we do not go to Him on our own. If He did not do what He does, we would never draw near to God—ever (John 6:44)! His work enables us to come into His presence.
Coming near to God is a priest's calling. A priest's work is essentially mediatorial. He stands much like a bridge between God and the people. This is keying us in to what our job is. We are to stand between God and the world. We have an awesome responsibility!
The English term priest comes from a root meaning "first," as in firstborn. A priest is one who comes first or goes first. He goes and then others follow. Our High Priest, Christ, is the first One in the presence of God eternally, never to leave.
We can draw near, but with our kind of character, as variable as it is, we come and go. We are like a ping-pong ball bouncing back and forth across a table. However, we still have the responsibility and the privilege of drawing close to God. He shows in the Old Testament ceremonies that we are supposed to go in prayer at least every morning and every evening, as pictured by the incense offering. David said he went before God "morning, noon, and evening."
"Priest"—or "first" (its root)—indicates a leadership position. Christ is our High Priest. He led us into the presence of God. We follow Him there, and we are, symbolically, very close to Him there. But we are leading others; they will someday follow us into God's presence. Even as Christ's work made it possible for us to get into the presence of God, so—in the future—Christ's work and our work will lead the rest of mankind into His presence. They, too, will have the same privilege that we do. So the whole church of the firstfruits goes first before God in behalf of the people who will follow at a later time.
When the priests in Israel drew near to God, they took with them the thanksgiving, the entreaties, and the sacrifices of themselves and of the people. However, this is a two-way street—or a bridge. They also brought back with them the gifts—namely things like reconciliation, understanding of God's will, and all kinds of other blessings of God.
John W. Ritenbaugh
New Covenant Priesthood (Part 1)