Two jobs, not one
An air conditioner moves heat from inside the house to the outdoor unit. As the indoor coil cools the air, moisture condenses on it and drains away, which is why a working system leaves a room feeling dry as well as cool. On a sticky August afternoon that second job matters almost as much as the first.
Size matters more than people think
Bigger is not better. A system that is too large for the house reaches the thermostat setting fast, shuts off, and starts again a few minutes later. It never runs long enough to dry the air, so the house feels clammy, and all that starting and stopping wears parts out sooner. A system that is too small runs all afternoon and still falls behind on the hottest days.
The right size comes from a load calculation, which looks at the house itself: its floor area, insulation, windows and which way the rooms face. Swapping an old unit for a new one of the same size, by default, can simply repeat an old mistake.
When it stops keeping up
Warm air from the vents, ice on the copper lines, water pooling near the indoor unit, a breaker that keeps tripping: each points to a different cause, and several are simple. Check the filter and the thermostat before anything else. If the system is past the ten-year mark, read up on what replacement involves before the next heat wave. If you are replacing anyway, a heat pump can take over the heating too.