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!