Is it like copper on the front, and maybe lead on the back? If so, it's what's called an electrotype, or "electro" for short. A wax impression is made of the set type. Next, the wax is treated with graphite and electroplated with copper. When the wax is removed, what's left is a thin copper shell which can serve as a printing plate. Usually, electros are backfilled with lead to give them added strength to stand up to the pressure of printing.
If it's solid, lead-like metal (type metal), then it was cast in a kind of thin papier mâché mould called a mat. The mat is created by impressing it upon set type while the papier mâché is still moist and pliable, then drying and curing it to withstand casting molten type metal into it.
If the condition's not too bad, any local newspaper or print shop should be able to pull a few proofs (printed copies) from it for you at little or no cost, and that would make a neat display with the plate itself.