If you try to set the option “delete it” from the Outlook Rules and Alerts wizard, you’ll get a message that that particular rule is “client-side only”, which means that Outlook has to be running for the rule to work.
If you’re trying to set up rules for mobile use, for example, this is less than ideal.
One workaround is to choose “move to a folder”, and move to the folder “Deleted Items”. This achieves basically the same thing, with the added bonus of keeping the message for review if needed.