what does the green knight represent in the story?
The Green Knight in Sir Gawain and the Green Knight (ca. 1360-1400CE) is most likely derived from a figure that appears in several earlier poems (for example, the French romance Caradoc) and throughout French and English folk tradition--sometimes called the Green Man, the Wild Man, or the Man of the Forest, and all of these, including the Green Knight, can be said to personify the force of Nature in conflict with mankind.
If we survey the scholarship on Sir Gawain, and the Green Knight in particular, we can find almost as many views of what the Green Knight represents as there are scholars who try to interpret the knight. The Green Knight has been interpreted as a form of the Green Man, a kind of vegetation God, whose use of the beheading game traces the figure back to pre-Christian Anglo-Saxon fertility rituals. Some critics see the Green Knight in a Christian context as Satan, whose goal is to entrap Gawain into a moral failure, either by committing a sin (with Lady Bercilak) against his host, Bercilak, or by failing to find the Green Knight's chapel in time. Other critics see the Green Man as a representation of Nature (in the form of the sun), which arises in the morning--as Bercilak does when he goes out to hunt--and returns every evening (the setting sun).
In the last few years, several scholars have convincingly argued that the Green Knight, who does indeed represent natural forces against civilization, is merely the vehicle that allows Sir Gawain, who learns a hard lesson about himself at the chapel, to evolve from innocence to what we could now call a "coming-of-age" state, that is, an awareness of how complicated life is going to be, and, more important, that he is not, and will never be, perfect.
On the most basic level, the figure of the Green Knight represents an insurmountable challenge; he entreats King Arthur's court to fight him on the promise that any knight may chop off his head, but in the following year, they must fight again and he will behead the knight. The entire court is so cowed by his proposal that Arthur is on the verge of accepting when Gawain volunteers.
On a deeper level, the Green Knight represents regeneration; he has an uncanny ability to restore himself, even to come back from what should be mortal injuries. Scholars equate the Green Knight with the "spirit of vegetation. Trees can live far longer than human beings, and they have regenerative powers that people have always envied" ("The Figure of the Green Knight," eNotes). His natural ability and regenerative powers combine in force to make a foe both daunting and formidable for Sir Gawain to overcome; in this way, Gawain's heroic deeds seem even more impressive.