The rich are rich because they're profiting from the poor; this can only happen in hierarchical relationships. The current system is in the shape of a pyramid: the bottom ranks make the most, but they're also the biggest rank, and so divided, they each make far less than the members of the topmost rank, who make the least, but divide that wealth between very few people. A huge amount of energy is being input by the bottom ranks, while the least amount of energy is being input by the topmost rank; the discrepancy is in why, despite each individual worker providing equal amounts of time and labor, some are paid very little, while others are paid a lot.
Socialism seeks to squash this divide; in the hierarchical system, you have a small group of owners who have the wealth to employ workers who generate more wealth for them; no business owner will ever hire a worker he cannot profit from. In the non-hierarchical system, each worker holds a stake in the company, and though they perform different jobs of varying intensity, they each get a fair cut in profits generated; if the company does well, they all become richer; if the company does poor, they all become poorer. This doesn't change the fact that company A can do far better than company B, but it certainly fails to centralize the world's wealth into a very small group of hands: it's not "Bill and Joe profits from Jason's and Lucy's labor", it's "Bill and Jason profit together, and Joe and Lucy compete with Bill and Jason."
I don't see anything wrong with voluntary poverty, don't get me wrong; if a person wants to be impoverished, that's his own business--perhaps he is a writer, or an otaku. My concern is for the people who work 8+ hour shifts every day and still have to look for more jobs to support themselves and their family, meanwhile those at the top of the system have more wealth than they know what to do with (usually involving empires and lobbying and such.) I don't find this agreeable; people who input a great amount of work should get a corresponding amount of profit.