A zafu is the round, firm cushion used for zazen. Its job is to raise the hips above the knees so that the spine can stay upright without strain.
Traditional zafus are stuffed with kapok. Many modern ones are filled with buckwheat hulls, which shift to fit the body and hold their shape. The zafu usually sits on a larger flat mat called a zabuton, which cushions the knees and ankles.
A cushion is helpful and not essential. A folded blanket does the same work, and sitting upright on a chair is a perfectly good way to meditate.