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 the king,
'bid me abandon this bench and stand by you there,
so that I without discourtesy might be excused from the table,
and my liege lady were not loth to permit me,
I would come to your counsel before your courtiers fair.
For I find it unfitting, as in fact it is held,
when a challenge in your chamber makes choice so exalted,
though you yourself be desirous to accept it in person,
while many bold men about you on bench are seated:
on earth there are, I hold, none more honest of purpose,
no figures fairer on field where fighting is waged.
I am the weakest, I am aware, and in wit feeblest,
and the least loss, if I live not, if one would learn the truth.
Only because you are my uncle is honour given me:
save your blood in my body I boast of no virtue;
and since this affair is so foolish that it nowise befits you,
and I have requested it first, accord it then to me!
If my claim is uncalled-for without cavil shall judge
To consult the knights draw near,
and this plan they all support;
the king with crown to clear,
and give Gawain the sport.
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.
Sir Gawain is basically demonstrating that he finds the Green Knight's request that someone take blows to him without the Green Knight responding until a year later, a folly. However, he wishes to honor those around him by taking on the task so they do not have to step down to such mediocre duty.
Sir Gawain is Arthur's nephew. He serves author as a royal and trusted knight. His greatest pride is as a chivalorous knight who honors the principles of integriety, piety, humility, loyalty, and honesty. He is a brave man but his life is important to him.