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The area of the tire that is in contact with the road surface at any given moment. The size, shape, and pressure distribution across the contact patch determine how much grip the tire can generate in every direction.
Guiggiani's The Science of Vehicle Dynamics provides the technical definition: "The contact patch (or footprint) is the region where the tire is in contact with the road surface. Most tires have a tread pattern, with lugs and voids, and hence the contact patch is the union of many small regions. The shape and size of the contact patch, and also its position with respect to the rim, depend on the tire operating conditions." Bentley puts it in driver terms in Ultimate Speed Secrets: "There are only four small tire contact patches that are actually holding you and your car on the road. The larger the contact patch, the more grip or traction that tire has. Increasing the tires' width obviously puts more tire footprint on the road." Jazar's Vehicle Dynamics Theory and Application adds: "The area of the tireprint is inversely proportional to the tire pressure. Lowering the tire pressure is a technique to increase the tireprint area." Every setup change — camber, pressure, load — ultimately works by changing how the contact patch interfaces with the road.