In Pride and Prejudice what does Darcy give Elizabeth after he proposes and what reason does he give for keeping Bingley away from Jane?

After Elizabeth's rather blunt and intense refusal to his
marriage proposal, Darcy drops by and gives Elizabeth a letter.  In the letter, he
explains his reasoning behind several key actions that had turned Elizabeth against
him.  In her refusal of his proposal, she said that she was upset that he conspired
against Jane and Bingley marrying.  She was also upset at the way he phrased things, as
if it was a pity move, instead of being motivated by love.  She also accuses him of
treating Wickham cruelly and unjustly.

Darcy comments on
all of these things, explaining that it was Wickham who was cruel, spending all of his
money and then going after Darcy's younger sister, manipulating her in hopes of marriage
in order to increase his fortune.  Then he explains that he did intervene on Bingley's
behalf, because he honestly felt that Jane did not care for him, and he wanted to
protect his friend's tender feelings.  He openly admitted that the behavior of her
family was embarrassing, and Elizabeth can hardly deny
that.

This letter changes Elizabeth's entire perspective. 
She realizes that Darcy is not the scounderel that she supposed he was, but rather a
true and loyal friend and brother, trying to protect those that he loves.  I hope that
helped; good luck!