Colonel Fitzwilliam is Darcy's cousin. Elizabeth is fond of him and he is a "good man." He develops feelings for Elizabeth, but he cannot be interested in her because he must marry for "wealth, not love" (eNotes).
Elizabeth rejects Darcy's first proposal because she still holds inaccuracies and judgments about him and his behavior. She also is angry because she feels he has turned Bingley against marrying Jane, which he did inadvertently. She still finds him to be conceited and gruff at this point, so although she has feelings for him, she turns him down.