Well, I would argue that what makes the figure of the Green Knight marvellous is the fact that a) he is green and b) he is apparently invulnerable to weapons and having various limbs and heads dismembered!
Critics have hotly debated his origins, but the fact that he is green suggests that he represents a spirit of rebirth and growth that is easily spotted in nature. For example, trees have the amazing ability to recuperate and grow back after being chopped down that we can see in the figrue of the Green Knight and the way that he treats his decapitation with nonchalance. Note how he simply picks up his head, which continues to operate normally, even though it is detached from the rest of his body, and carries on with his life. Interestingly, the next time he appears it is firmly stuck onto his body again where it belongs.
These two aspects, to my mind, are what makes this figure truly marvellous and amazing.
Tnx, but you didn't answer my other part of the question, what is his purpose in the poem??