After the brief introduction of the miracle of Christ's birth, the angel does two important things. The first is to identify the baby as the one who would fulfill the Messianic role, and the other is to clearly identify the Eternal Father as the very father of the child.
The Messianic role is implied in the "Lamb of God" title by which Jesus is introduced. To Nephi, familiar as he was with the sacrificial laws of the Law of Moses, he could not have missed the import of the sacrificial lamb. That lamb under the Law would remove sin, this child, as the Lamb of God would do so in a way grander and more effective than all of the previous lamb offerings.
The angel then continues to make the clear association of Christ and the tree by immediately tying the vision of the birth of the Savior back to the tree. Note again, however, that it is done with a question. Even in vision, Nephi must work our much of the meaning for himself.