Rootstock is the part of a grafted vine that grows underneath the surface. Almost all vines planted today are grafted onto different species of what we in general call American rootstock (Vitis Laparia, Vitis Rupestris, etc). These are different varieties of the Vitis family, and they are resistant to Phylloxera. All noble varieties used for wine production, e.g. Chardonnay, are from the Vitis Vinifera family, but not resistant to Phylloxera.
In order for them to survive, they are grafted onto a suitable rootstock either before planting or in the vineyard. Different species of rootstock are more or less vigorous and better adapted to a certain climate and soil, and it's crucial that the noble variety is paired with a suitable rootstock according to the style of wine you want to produce.