Red wine is wine made predominantly from red grape varieties which has been fermented to dryness, meaning it has little or no residual sugar in the bottled wine.
Like other dry wines in general, all the sugar in the grapes have been fermented completely to alcohol. Most red wines are dry, with the exception being some dessert styles of red wine such as Port.
Most red table wines, such as Cabernet Sauvignon, Merlot, Zinfandel, Pinot Noir, Syrah and wines from these grapes such as Bordeaux and Burgundy, are completely dry.
Red table wine can vary from light fruity wines to rich, full-bodied wines and everything in between. The particular style is a function of the wine growing region, the grapes used, the winemaking style and other factors.
Calling a wine dry simply means it has little or no sugar in it. However, tannins, naturally occurring compounds in grapes which are common in red wines and contribute to the structure and texture of the wine, are often described as drying or making the mouth feel dry.
Most typical red table wines are dry. They vary considerably. Whereas a good young Beaujolais from France may be light-bodied, fresh and fruity, a great, young Bordeaux (made mostly from blends of Cabernet Sauvignon, Merlot, Cabernet Franc and other grapes) can be quite large-scaled with big rich, deep, dark flavors and considerable tannin.
Somewhere in the middle, Pinot Noir based wines such as red Burgundies are generally less tannic and muscular than Bordeaux with a silkier texture, finer tannins and higher acidity and brightness. There is a whole world of dry red wine out there with various styles and flavors so it is hard to generalize.
Also, in addition to the effect of tannins, dry wines can vary in how dry they seem even if they have essentially zero residual sugar.
Dry red wines are often very good with food if you pair them wisely.