A wedge is a thin triangular piece of wood or metal that is driven into another material in order to widen the material. This may cause the material to crack (in the case of stone) or two tighter the fit of a material into another (ie when fitting the handle of an axe).
Wooden wedges are cheap, easy to make, and expand and contract at the same rate as the wood of a handle. They are made using a slender piece of wood of the same width of the eye. Take a chisel and push the blade of the chisel along and into the surface to remove the end material. Taper the end slightly to that it fits into the channel in the wood easily, add glue to the wedge (hide is nice but stinky) and drive in with a mallet. Ensure that the channel is cut across the grain.