The resonator absorbs some of the noise from the exhaust before it gets to the muffler... having just one or the other will make the car slightly louder... and slightly more powerful.

A resonator is basically a straight tube with holes in it, leading to the resonance chamber (the body of the resonator)... sound waves travel through the holes and into the resonance chamber. There are two ways a resonator can go bad... it could be that it's a glass-packed resonator and that the packing-material is rotting or disintegrating... this will make it noisier, but not necessarily stuck up... or the welding on the resonator tube is coming apart, which could lead to the packing material escaping out through your tail-pipe. This will also cause turbulence inside the resonator, which you will feel as a loss of power.

If this is a catalytic converter, though, and not a resonator... that can go bad, which will cause a loss of power, and cause restriction in the exhaust.

In other words, if you don't feel a loss of power... don't worry about it.