What does Process in nm mean?(45nm,28 nm)

What does manufacturing process in nm mean in processors?

The snapdragon S1 and S2 are 45nm

S4 is 28 nm

Sandy bridge 32nm

Ivy bridge 22nm

So is a smaller process better?

I've read somewhere that it lowers power consumption, is smaller, saves space.

Are there any other advantages?

And why does it have these advantages?

can anybody explain?