How does this clamper circuit work?
I think you got it. It is a V2 clamp. Node 1 will follow V1 for small voltages until V1 gets to be larger than 1V + VF(diode) ~ 1.7V. If V1 continues to increase then D1 (and V2) will sink the necessary current to keep node 1 at 1.7V. Hope that helps.

EDIT: After clamping node 1 for the first time, the AC capacitor will charge up. If this charge doesn't leak, node 1 will now have an offset equal to the voltage difference between V1 and the initial clamp voltage. As the other answer states, this is often used as a charge-pump offset generator