Grafting is the process of connecting together 1 piece from 2 different plants to make one living plant. This is an important practice in modern viticulture since it was discovered in the 19th century to be the best defense against phylloxera.
Today, most plants are grafted throughout the world specifically to prevent phylloxera. Here a North American vine species (vitis lambrusca, vitis riparia and especially vitis rupestris) is used for the bottom vine (or rootstock) and the higher quality European species (vitis vinifera) is grafted on top (the scion). This is because North American vine species will form a scab over the feeding area of the phylloxera louse and prevent it from dying.
Nowadays, the grafting business is fully evolved. Viticulturalists will choose various rootstocks for soil suitability, frost prevention or to control vine vigour. They will order fully grafted vines from vine nurseries.
Although most grapevines of the world are grafted, many wine conoisseurs believe ungrafted vines produce the higher quality wines.
Making wine from ungrafted vines is therefore a marketing point for those producers. See phylloxera.