It's just a way of measuring inner diameter of a gun barrel and thus the size of ammunition required.

The reason it's inverted from what you'd expect is because it's based on how many spheres of that size you could make with one pound of lead. This is speculation, but I think it's a hold over from very early firearms; cannon bore was measured in pounds of iron in a spherical shot, so when making smaller guns they'd have naturally moved to measuring what fraction of a pound constituted one shot. It's really only used for smooth-bore guns, not rifles, because the varying length and profile of a conical bullet would make the weight-diameter relationship meaningless.

Edit: Cannonballs are measured in iron, not lead, pounds - but the historical connection seems solid.