A little plastic box (about 4 cubic inches), full of goodies required to repair a hole in an inner tube. Most useful for bicyclists.
Patch kits usually contain rubber cement, a piece of sandpaper, and a couple of patches of different sizes.
The rubber cement, of course, is used to attach the patch to the inner tube.
The sandpaper is there to either roughen the inner tube to help the glue adhere, or remove the mold-release compound, depending on who you believe. I believe the latter. They coat the mold they make the inner tube in with the stuff so that the inner tube will come off the mold. Likewise, the stuff will probably prevent the patch from sticking.
The patches plug the hole. Use the size that best fits the hole. Patches have metal foil on one side, and clear plastic on the other. You don't have to get rid of the clear plastic, but the metal foil is on the surface that goes on the rubber cement, so you must of course remove the metal foil.
Not to be confused with a sew-up patch kit, which contain needle and thread, along with the stuff mentioned above. You need the needle and thread to repair flats in old sew-up tires that hardly anyone uses anymore.