What does the ‘press saver’ setting on my dryer do?

It stops drying your clothes right before they are completly dry so you can hang them and avoid the need to iron them. It is a great option!!

From the manual:
Select Press Saver if the dried load might not be
removed promptly at the end of the cycle. The dry
load will continue tumbling without heat for 30
minutes to help reduce wrinkling. When the Cycle
Signal is selected, a beep will be heard periodically.
The load may be removed any time during Press
Saver.

It also keeps the drum turning after the cycle is over so that the clothes don’t sit in a pile and get wrinkled.