First, the name "Jesse Tree" comes from Isaiah 11:1-2
A shoot will come up from the stump of Jesse;
from his roots a Branch will bear fruit.
The Spirit of the LORD will rest on him—
the Spirit of wisdom and of understanding,
the Spirit of counsel and of power,
the Spirit of knowledge and of the fear of the LORD -
The idea, of course, is that Christ came from the "stump of Jesse" (Jesse's "tree", get it?), and all of the Old Testament points toward the coming of Christ as Messiah.
To summarize, we will put a two-foot tree on a table in our living room, and beginning on December 1, we get out an ornament each day. The first ornament represents creation, and we read a little devotional on creation. Then each devotional takes us through the Old Testament, showing how it all pointed to Christ, until Christmas Eve, when we finish by placing the star on the top of the tree. I think this is a great idea that will teach our family a great deal! I am so excited...Now, if I can just get it all together before Dec. 1.
Here is a link that describes the Jesse Tree.
Jesse Tree Family Devotions: Advent 2006