Elizabeth, as the title of the novel indicates, develops a prejudice against Mr. Darcy after overhearing him say she isn't pretty enough to tempt him to ask her for a dance. She finds him a proud and disagreeable man, as do most of her neighbors. She has been insulted, as any young woman would be, and finds it difficult to get over this first, negative, impression.
Mr. Wickham, however, is charming to Elizabeth during their first meeting, as well as being very handsome. He focuses attention on her and makes her feel attractive. When he begins to complain about Mr. Darcy treating her unfairly, this fits in with the impression of Mr. Darcy she has already received. Mr. Darcy already seems to her to be a person who is harsh and unfair, and Wickham seems sensitive and agreeable.
Today, we call this confirmation bias. We are often eager to find confirmation for what we already "know" to be true rather than to have our knowledge challenged. Elizabeth is already biased against Mr. Darcy, and Wickham's story fits perfectly with the narrative she has constructed about this proud man. She has every reason to want to believe it because it helps justify her dislike of Darcy.
Very interesting question. You may find it very useful to know that originally Jane Austen wanted to call this novel First Impressions, which obviously places far more emphasis on one of the key themes of the novel - the extent to which we make judgements based on first impressions. Another key element of the novel, as highlighted by the title we have now, is the prejudice that Lizzie displays in her quickness to judge Mr. Darcy, and write him off as an arrogant man.
Of course, the first sight we have of Darcy is that of a very proud, disagreable man. In the assembly ball, he refuses to dance with anyone except women of his "class", is harshly judgemental about the beauty of Lizzie and so we, like the Bennets, agree with Mrs. Bennet´s assessment of the man:
"...for he is a most disagreeable, horrid man, not at all worth pleasing. So high and so conceited that there was no enduring him! He walked here, and he walked there, fancying himself so very great!"
Of course, as Lizzie goes on to discover through the course of the novel, this exterior to Darcy reveals the sensitive, caring, compassionate and honourable man underneath. But it is important to see how the author is playing with us as she plays with her characters in their assumptions. Mr. Wickham, when he is introduced, is featured as the exact opposite of Mr. Darcy - they are foils of each other:
His appearance was greatly in his favour; he had all the best part of beauty, a fine countenance, a good figure, and a very pleasing address.
Thus we can see why all the characters are so easily taken in by Mr. Wickham´s appearance, and because of our first introduction to Mr Darcy we, like the characters, are more than willing to believe Mr. Wickham´s fabricated account of how Darcy disinherited him. As Lizzie later comments once she knows the truth of their characters:
One has got all the goodness, and the other all the appearance of it.
Of course, the message is clear - Jane Austen is challenging us just as much as her characters to not go by first impressions and to look deeper, witholding judgement until we have more evidence. This is a lesson that Lizzie Bennet painfully learns, enabling her to marry her true love by the end of the novel.