In regards to themes, Mr. Wickham represents several different thematic points that Austen is making in the novel. Here are two of them. The primary theme of the novel is the importance of marriage and the motivations for marriage. All of the women that draw Wickham's attention are examples of marriage for wealth. While the relationships, if you can call them that, with Miss King and Georgianna Darcy fail, his motivation is financial. Even his eventual marriage to Lydia comes about because Darcy offers a very handsome financial pay-off to make the scandal go away.
Austen also uses Wickham to illustrate her themes of pride and prejudice. Elizabeth believes Wickham's lies about Darcy and finds Wickham to be a very charming man. Because she believes his tales, she is even more prejudiced against Darcy than she was at the start of the novel. Elizabeth is prideful in thinking that she has everyone all figured out, and once she realizes how wrong she was to believe Wickham, her pride is brought down a notch and her prejudices against Darcy fade away.
Themes, as far as the different stories within the novel are plenty:
He was once involved with Georgiana Darcy, the younger sister of Mr. Darcy, and enticed her to elope with him just for the sake of getting back on Mr. Darcy, whom he despised.
Then, he tried to get engage to Ms. King, who was a rich heiress and whom he did not love, only to get her money. When she realized he was a nobody, they broke up.
After that, he did the rounds on Elizabeth, telling her his sad story about how Mr. Darcy and he had grown up together and that Darcy was jealous of him and sent him to ruin. The reality was different, since Darcy had offered Wickham a job as a clergyman but, instead, Wickham took his share of the inheritance once Darcy's dad died, spent it all, and came back for more only to be sent away.
The worst one was when he befriended Elizabeth's sister, Lydia, who was but 15 years old and dumb enough to actually be dazzled by Wickham's uniform. When she eloped with him, she thought he would marry her, but he was not planning on it. After Darcy intervened, paid a dowry and made Wickham marry Lydia, was when the reputation of the Bennet sisters was saved.
In the end, he was bold enough to still call Elizabeth "sister" afte he returned with Lydia for the post-wedding reception, and saw in Elizabeth's eyes that she was very clear of the type of scum he was.