The rootstock is a plant chosen on its merits during grafting to become the roots of a new plant. Rootstocks will have been chosen for their disease resistance, vigour, or the eventual height.
For example, fruit trees are grafted onto rootstocks which determines the eventual height of the tree. A cordon apple tree of the Lord Lambourne variety needs to be small, so a dwarfing rootstock such as M27 may be chosen. This means the tree should only grow to about 6-7 feet high. If a different rootstock was chosen, say M26, then the same Lord Lambourne apple variety would grow to 10-12 feet tall.
Many roses are grafted onto a different rootstock to improve their disease resistance. Species roses are not grafted.