Bent gently within its own curve, nothing; the core is designed to flex that far and springs back. Bent sharply, or against the direction of its curve, the core takes a set, and the chain no longer returns to a smooth arc but holds an angle at that point.
The plates either side of the bend are pushed apart on the outside of the angle and crowded on the inside, which shows as a gap or a step in the mirror surface. On a flat omega the edges of the plates can lift.
A jeweller can sometimes ease a mild kink out of the core and reseat the plates, but a sharp bend is usually permanent. Prevention is simple: the chain is put on and taken off open, never pulled over the head, and stored flat.