The casing of a cross-ply tyre consists of a number of rubberised cord plies with edges wrapped around the bead wires. (The bead ensures that the tyre sits firmly on the wheel rim).
The number of plies determines the load capacity of the tyre. Cross-ply tyres for passenger cars generally had between two and six rayon or nylon cord plies. Even today, van tyres are said to have 6 or 8 plies, with a higher number of plies meaning a greater load-carrying capacity.
Cross ply tyres are nowadays few and far between on modern cars, having being replaced by radial construction.
Diagram shows a typical cross ply tyre construction. The angle of the plies determines the stiffness of the tyre. The sharper the angle, the stiffer the casing. As you can see a racing tyre, requiring high stiffness, has the lowest of ply angles.