Personally, I think immunity to normal weapons is too broad of a power. A lot of non-magical weapons have forms of attack (fire, sonics, etc.) that I feel would fall under different categories of immunity. I personally think it should only work against non-magical physical attacks such as blades, bullets, etc. and not apply to things such as electricity or acid. Purely by RAW, though, it works against any attack that is not explicitly magical.
That's what I always assumed it meant. I've always only applied it to bullets, knives, fists, etc. I typically include explosions and grenades as well.