A crossflow cylinder head is a cylinder head that features the inlet and exhaust ports on opposite sides. The gases can be thought to flow across the head. The crossflow head is in contrast to cylinder head designs that have the ports on the same side.
A crossflow head gives better performance, but the popular explanation put forward for this - that the gases don't have to change direction and hence are moved into and out of the cylinder more efficiently - is largely erroneous, since there is no continuous flow because of opening and closing of the valves. The main reason for a crossflow's performance is that the ports and valves can be larger. Most modern engines used in cars are of a crossflow design.