Like Gurth, Wamba is a servant/slave to Cedric. Wamba (son of Witless) is a fool – kind of like a medieval comedian. He's Cedric's live-in joker. We would be more jealous of Cedric having a comedian on hand 24/7 if Wamba were actually funny. He specializes in comic songs about knights, ladies, and monks (basically, the same kinds of characters we see throughout Ivanhoe).
We should note that a lot of the characters in Ivanhoe imply that Wamba is developmentally disabled. He had a childhood illness with a high fever that damaged his brain. However, we see no evidence that Wamba's illness has damaged his ability to make up complex songs or puns – he's much more poetic than the majority of guys in this book.
Wamba's ballads imitate the style of medieval songs as Scott imagined them. They come across as really dated, and probably did even back when the book was published. We don't mean to be harsh, but the comedic possibilities of a widow marrying for money instead of glory seem fairly limited to us.
What makes Wamba important to the structure of Ivanhoe is not his sense of humor; it's his social position as a jester. There's a long literary tradition of "the fool" in English literature (check out Feste in Shakespeare's Twelfth Night for example). Since jesters and comedians are, by definition, not meant to be taken seriously, they can often say things that other more serious characters would be punished for.
If you're looking for a contemporary equivalent to Wamba's social role, think of Jon Stewart over at The Daily Show. Stewart can say crazy stuff about contemporary politicians because he is a comedian and everyone takes what he says with a grain of salt. If Stewart were a straight-up journalist, his comments about politicians' private parts would probably not fly.
Wamba is like Ivanhoe's Jon Stewart – except, you know, a lot less smart and funny. He can make jokes about the Normans to their faces (like when Bois-Guilbert and Prior Aymer meet him in the forest in the early chapters of the book) and not get killed for it. Wamba's jester's uniform protects him from punishment for speaking plainly.
We have one last thing to say about Wamba. Even though he jokes pretty liberally about the Saxon/Norman situation, he really wants to maintain conservative master/servant bonds. Wamba is by no means about social change. When Wamba's master, Cedric, is being held captive in Torquilstone, he insists on taking his place in disguise to save Cedric's life – even if it means Wamba's own death. And when Cedric offers to set Wamba free in exchange for his help against the Normans, Wamba actually refuses. He likes the security that belonging to Cedric's household gives him, even if it means that he stays a slave. So in that respect at least, Wamba truly is a fool.