Why outside
It removes the finest dust that gets past the filter, along with warm air and some noise. Manufacturers generally recommend it where practical. Check the manual for your model.
How it is done
A short pipe from the unit's exhaust port to an exterior wall, with a vent cap. An inline muffler can reduce noise outside.
When indoors is fine
If there is no practical route, units exhaust through their own muffler. Keep the filter clean.