In Sir Gawain and the Green Knight, Gawain travels to meet the Green Knight so that the other may take his turn at beheading Gawain, as they had agreed a year prior. Gawain arrives at his destination early. Finding a castle nearby, he requests the lord's hospitality, which is eagerly granted.
The lord is Bertilak (secretly the Green Knight, a shape-shifter). He welcomes Gawain, and suggests that while he passes the Christmas holiday with the lord and his wife (Lady Bertilak), that they share the fruits of their labors each day. So when Bertilak goes out hunting the first day, he returns with his kill which he presents to Gawain. In the meantime, Lady Bertilak has been attempting to seduce the noble Gawain, but he resists, exchanging only a kiss. When Bertilak returns, Gawain presents the kiss he has received that day from the lady, to his host. The next day it is two kisses, and a different animal. The third day, three kisses, and a fox.
In all of these situations, Gawain is honest with Bertilak (except for the magic sash which is supposed to save him from death—he hides this). In the life at court, a kiss was not a betrayal, and Gawain returns the kiss/kisses to Bertilak each day.
If we are looking for symbolism for the three kisses, we might look to the three temptations of Christ by the Devil. First he tempts Christ to prove himself by turning stones to bread. Jesus refuses. Satan's second temptation is that Christ throw himself down from the top of the temple, for surely God's angels will save him, but Jesus refuses. The last temptation is an offer: Satan takes Christ to the top of a mountain and promises that Christ will be lord of all he sees if he will bow down and worship Satan. A third time, Jesus refuses.
Literally, Lady Bertilak tempts Gawain three times. Figuratively, this may be an allusion to the three temptations of Christ—remember that Gawain, as a true knight, serves not only Arthur, but more importantly has taken an oath to the Church; his patroness is the Virgin Mary. All he does is in service to her, and she inspires him.
Gawain is tempted three times with three kisses; he does not keep them for himself, but returns them to Lord Bertilak. Bertilak later admits that he used his wife to help test Gawain to see if he was as noble, honorable and trustworthy as Arthur's knights, especially Gawain, were reputed to be.
Whether as simply a literary figure, or as a symbolic character compared to Christ, Gawain withstands temptation.