A hybrid is when a grape variety from one vine species crosses (or breeds) with another vine species. This can happen either naturally by cross-polination or deliberately by people in a vine nursery.
(Note: the EU prefers the term interspecific crossing.)
The most important examples of hybrids are from the 19th century when Europeans looked for a cure for phylloxera and the other scourges of the time (powdery mildew, downy mildew, and black rot).
Scientists learned to cross a vitis vinifera vine (the European vine species) with a North American species (such as vitis riparia) to try to get the best of both worlds. Vine breeders want the quality and flavour of the vitis vinifera European species combined with the disease resistance of the American species.
Wines made from hybrid varieties are generally thought to be of lesser quality by wine connoisseurs.
Yet, many hybrids are more disease resistant and require less chemical sprays (fungicides, pesticides, etc) than vitis vinifera. Therefore, many proponents of organic viticulture now recommend planting hybrids over vinifera (especially in the New World).
In the Old World, most wine laws are written to exclude hybrid varieties from all quality wine designations. They are instead relegated to the lowliest ‘Vin de Table’ category (with few exceptions).
Hybrids are however commercially available worldwide as rootstocks.
In the search for the cure for phylloxera in the 19th century, scientists found that by grafting vitis vinifera onto American rootstocks, they could save European vineyards from devastation. As time went on, nurseries developed better hybrid rootstocks to fit specifically with certain soil types, varieties, and diseases.
Today almost all vitis vinifera (Cabernet Sauvignon, Sauvignon Blanc, Chardonnay, etc) are grafted onto hybrid rootstocks to prevent phylloxera and other diseases.