According to JMDict 予約 is translated as
- reservation; appointment; booking; advance order
- contract; subscription; pledge
None of the meanings above seem to make sense to one of the function labels on a washing machine.
On Japanese washing machines the 予約 is designed to set a timer for the washing machine to start. For example, if you don't want wet clothes to be in the machine while you're at work you can put clothing in there, set a 予約 timer for a an hour before you return and then it won't start the cycle until then.