Short answer:
A proof house is where they take the guns to test them with an over load,or as some people might say,to try to destroy them
In this country,we don't have proof laws,relying on the manufacturer to test and put out a safe product themsleves.
Underwriters Labratory could be considered a proof house for things other than guns.
Most European countries have what are called proof laws.These laws require all guns to be submited for prooving their safety before they are sold.
The proof pressure is set in the laws most of the time,usually 50%-100% overload.
The "P" on most US Military guns is a proof acceptance marking.
Same thing with the "P" on Winchester barrels.
There is view proof meaning it looks okay and the parts are correct,several
layers of firing proof,one for unfinished barrels (used on shotguns and maybe others) sometimes a final proof of the just the barrels,and a final proof of the whole gun.
Guns that are sold in another country will sometimes have to be reproved in that countries prooving house also.I had a FN made Browning 25 that had Czechoslovakian
proof marks on it as well as the Belgian ones.
I'm sure I left something important out,but that is an overview.