A washer that finishes its cycle with water still in the drum has either lost the ability to pump, or has somewhere for the water to go but cannot get it there.
Blockage or pump
Listen at the point in the cycle when it should be draining. A drain pump that is trying to run makes a distinct humming or grinding noise. If you can hear it working but nothing moves, something is blocking the path. If it is completely silent, the pump itself, the control board, or the wiring to it has failed.
A blocked pump filter is far and away the most common cause, and on most front-loaders it is behind a small hatch at the bottom front of the machine. Coins, buttons, hair clips and screws all end up there. Have towels ready — there will be standing water behind it.
The drain hose
If the filter is clear, the hose is next. A kink behind the machine, a blockage where it joins the standpipe, or a hose pushed too far down the standpipe will all stop the water leaving. If the hose outlet sits too low relative to the drum, the machine can also siphon, which produces different but equally confusing symptoms.
When the door will not open
Many machines will not release the door while they detect water inside, which is a safety interlock rather than a fault. Draining the machine through the filter hatch usually releases it. Forcing a locked door damages the interlock and turns one repair into two.
Less common causes
A failed pressure sensor can leave the machine believing it is still full, so it never advances to the spin. A control board fault can stop the drain signal reaching a perfectly healthy pump. Both look identical from outside the machine and need testing to tell apart.
Before you call
Clearing the filter is worth doing yourself and fixes a good share of these. If the filter is clear and the pump is silent, it is a parts-and-labour job rather than a five-minute fix.
Getting it looked at
This is general guidance, not a diagnosis. The same symptom can have a cheap cause or an expensive one, and the only way to know which is to have someone measure it. A technician will find the actual fault and give you a fixed price before any work starts, so you can decide with a real number rather than a guess.