DIAGNOSIS The drain pump is either clogged or has failed. A clog is way more likely—something like a small sock, hair, or a coin has jammed the impeller.
FIX Unplug the washer. You'll need to access the pump, which is behind the lower front panel. Remove the panel (usually a couple of screws at the bottom edge, then slide it down). You'll see the pump at the bottom. Place towels underneath. Disconnect the drain hose from the pump (clamp) and the wiring connector. Check the pump inlet and impeller for obstructions. You can often spin the impeller by hand to feel for a blockage. Clear anything you find, reconnect everything, and test.
IF THAT DIDN'T WORK If the pump is clear but still won't run, the pump motor itself might be dead. You can check for continuity with a multimeter, but usually, if it's getting power (you might hear a hum) but not spinning, the motor is seized or burnt out and needs replacement.
HEADS UP Before you start, bail out as much water as you can from the tub with a cup or small bucket to minimize spillage when you disconnect the hose. And remember, even unplugged, there might be residual water in the hoses.