Monsieur Mabeuf works at a church is Paris, and he shows up as the recipient of Valjean's generosity and the provider of key info to Marius—namely, that Marius's dad loved him after all. He might seem like a bit player at first, but Hugo uses him in a lot of deep symbolic situations throughout this book.
For starters, Mabeuf is your typical non-political thinker. He doesn't want to get mixed up with all the messy politics of his time. All he wants to do is read books and keep his head in the sand (like an ostrich). As the narrator says:
He could not understand why men should expend themselves in fury over such trivialities as the Charter, democracy, monarchy, republicanism and so forth when there were mosses, grasses, and shrubs for them to look at. (126.96.36.199)
In another passage, we read that "The sight of a sabre or musket chilled his heart" (188.8.131.52). Mabeuf likes books and plants, and that's all he really cares about—at least for most of the book, even as he's slipping into poverty. As we read at one point, "Thus it was that with the shadows deepening about him, with his hopes fading one after another, Monsieur Mabeuf had remained serene, rather childishly but profoundly so" (184.108.40.206).
As time passes, though, Monsieur Mabeuf falls deeper and deeper into financial hardship until he has to sell all of his favorite books and abandon his garden. It's only when the guy has nothing left to lose that he has a shift in his ideas. By the end of the book, Monsieur Mabeuf has joined a group of French rebels. He even sacrifices his life for hoisting the Republican French flag, shouting at the top of his lungs: "Long live the Revolution! Long live the Republic! Fraternity, Equality – and Death!" (220.127.116.11).
The moral here? Well, there are two related ones: (1) avoiding politics sounds nice and relaxing in theory, but eventually the world's going to make you stand up for something; and (2) if you take everything away from people until they literally have nothing to live for, you shouldn't be surprised if they're willing to die fighting you.