This is yet another symbol often interpreted (by Christians) as referring to Jesus:
A shoot shall come out from the stump of Jesse, and a branch shall grow out of his roots. The spirit of the Lord shall rest on him, the spirit of wisdom and understanding. (Isaiah 11:1-3)
(The Gospel of Matthew tries to trace Jesus's genealogy back to King David—and by extension, Jesse, since he's King David's dad.)
The shoot also harkens back to an earlier idea in Isaiah 6, where God says that Israel will be so terribly burned and ravaged that it will be reduced to nothing but a stump, though the holy seed is (or, is in) the stump. This fits in with Isaiah's whole discussion of a saving remnant: all the good and righteous people will be preserved and will endure to participate in a future age of peace. The shoot symbolizes then the Messiah, or the righteousness of the people as a whole. It's the goodness that's left over, and that remains to flourish.