To resign is to quit or retire from a position. You can also resign yourself to something inevitable, like death — meaning you just accept that it's going to happen.
When people resign, they're leaving something, like a job or political office. Congressmen resign after a scandal. Coaches resign after a really terrible season. Regular folks simply resign when they're ready to go. In those cases, resign is a nicer way of saying quit. Being resigned is another sense of this word — it's a type of acceptance. If your team is losing 80-20, you might as well resign yourself to losing. That just means you aren't in denial.