Stationary Point
A point where the gradient is zero, so the surface is momentarily flat — a minimum, a maximum, or a saddle.
A zero gradient means no direction is downhill, so gradient descent stops moving. What it does not mean is that you have arrived somewhere good — the gradient alone cannot distinguish a minimum from a maximum from a saddle. That takes curvature, which is what the Hessian supplies.
The folk story that training gets trapped in bad local minima is largely wrong for deep networks, and the reason is a counting argument. For a stationary point to be a local minimum, the surface must curve upward in every one of millions of directions. One direction curving down makes it a saddle instead. Saddles are therefore overwhelmingly more common, and a saddle is escapable — there is a way down, it just takes a while to find.
The practical symptom is a loss that plateaus rather than one that stops permanently. Momentum helps precisely because it carries speed through regions where the gradient is nearly flat.