Christians are familiar with this passage from its presence in Advent and Christmas readings. It is often regarded as a prophecy that was fulfilled when Jesus, the Messiah, was born in Bethlehem. Though Jesus does not look like the kind of messiah that people were looking for, he did meet the requirement that he be descended from David. The genealogies in Matthew and Luke make that point. More, the narratives in Matthew and Luke place his birth in Bethlehem, reinforcing his legitimacy as a son of David. The everlasting covenant that God made with the house of David was still intact. It had only been set aside temporarily during the years of exile and for several more centuries.
The prophecy states that the one who is to rule in Israel has his origin "from of old, from ancient days." This probably is a reference to the ancient promise to David that his sons would rule on the throne of Israel forever (2 Samuel 7). Though a break in the dynasty had occurred, the promise had not been broken. When the Christians applied this passage to Jesus, it put him in continuity with the Davidic promise. As the belief in a preexistent Christ (Messiah) developed, God's messianic work was pushed back even further into the past, not just to the time of David but to the presence of Christ in heaven with God. In the apocalyptic vision of Daniel 7:9-10, God is called the "Ancient One" (or "Ancient of Days").
who are one of the little clans of Judah,
from you shall come forth for me
one who is to rule in Israel,
whose origin is from of old,
from ancient days.
3 Therefore he shall give them up until the time
when she who is in labour has brought forth;
then the rest of his kindred shall return
to the people of Israel.
4 And he shall stand and feed his flock in the strength of the Lord,
in the majesty of the name of the Lord his God.
And they shall live secure, for now he shall be great
to the ends of the earth;
5 and he shall be the one of peace.
If the Assyrians come into our land
and tread upon our soil,*
we will raise against them seven shepherds
and eight installed as rulers.
New Revised Standard Version Bible: Anglicized Edition, copyright © 1989, 1995 National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved worldwide. http://nrsvbibles.org