What do we learn about Sir Gawain's character from this selection from Sir Gawain and the Green Knight?'Would you, my worthy lord,' said Wawain to...

We learn several things about Sir Gawain from this passage in Sir Gawain and the Green Knight.

Gawain fulfills the requirements of chivalry in this passage.  The challenge by the Green Knight is below the exalted King Arthur, says Gawain, so he politely requests that the king allow him to take up the challenge.  Gawain says he knows that he is the least of all the knights present, and that the only reason he is anything at all is because he is related to King Arthur.  The challenge is more fitting for Gawain to accept, than it is for King Arthur.

We learn, then, that Gawain is honorable, considerate, polite, and humble.  He is a chivalrous knight of the round table.