A load that ends with water still in the drum is a clear sign that something in the drain path is not doing its job. The fault can be simple, and you can usually narrow it down yourself before you call anyone. Work through the checks in order.
Listen to the cycle
Start the drain step and listen. A pump that hums and moves water points away from the pump itself. A pump that runs but moves little water points to a restriction in the hose, the filter, or the standpipe. A pump that stays silent points to the power, the control, or a door or lid signal that never completed. Note which of these you hear before you move anything.
Check the drain hose
Pull the washer away from the wall only as far as the hose allows. Look for kinks, flattened sections, and a hose that drops below the water line or rises too high. Confirm the hose is seated in the standpipe or drain and that the end is not wedged against the wall. Clear the hose of any blockage you can reach.
Clean the drain filter
Many front-load and some top-load washers have a drain filter behind a small access panel near the base. The machine's manual shows where it is. Place a shallow pan and towels first, because the filter holds water. Remove lint, coins, hair, and small objects, then replace the filter firmly.
Look at the standpipe and the sump
Check that the standpipe is open and that it is not clogged with lint from the wash. If the household has had slow drains elsewhere, the trap or the wall drain may be the real restriction, and that is a plumbing question rather than a washer question.
Decide what to ask next
If the hose, filter, and standpipe are clear and the pump still moves no water, ask the repair person to test the pump, the drain valve, and the control. Ask them to write down which part they checked and what they found. If the pump runs and the water still will not leave, ask whether the drain path has a restriction the washer cannot clear on its own.
The clothes washer page on this site lists typical service life and the planning points for the machine. Use the install year as your starting point when you decide whether a repair or a replacement makes sense.