what does the green knight set out to test?

The Green Knight wants to test the courage and integrity of King Arthur. He settles for Sir Gawain instead.

Just in case you need to know the backstory:

Green Knight bursts into all the Knights feasting (Christmas Eve or New years I think). He challenges Arthur but a good knight doesn't let his king battle first. So Gawain entertains the challenge. It ends up being a challenge of honour more than anything else. Will the knight live up to his strict code? Will he give the Green Knight everything he is given? It's that sort of thing.