The deep meaning

Loosely speaking it means "evidence of guilt," since a smoking gun is evidence that it was fired.

Indisputable evidence (especially of a crime)

Right. It means evidence that proves that a crime took place (and usually implies that the criminal has been found).

It comes from the fact that after a gun has been fired, smoke comes out of the barrel.

So imagine a scene where there is a closed room with 12 people in it, the lights go off, and there is a gunshot. Then the lights go back on, and someone is dead. Everyone insists that they are innocent, they didn't shoot, but then behind one person's back is found a smoking gun. The smoke means it was recently discharged. That person is guilty.

That's not perfect, but hopefully gives an idea. This is definitely one of those questions that are harder to answer than I expect when I start!

Ah, should've waited, nice pithy responses while I was typing. ;-)

Thanks!
Thank you very much !