Multiculturalism is simply the presence of multiple cultures. According to Jonathan Haidt, one of the differences between liberals and conservatives is that liberals love new experiences whereas conservatives hate new things and want everything to stay exactly the way it looked like on TV when they were growing up.
So liberals love diversity, because it means they can gentrify a crappy neighborhood and enjoy burritos for breakfast, falafel for lunch, and a lox-bacon-cream-cheese bagel for dinner. They get to enjoy finding new and different things around every corner, and they get to make friends with people whose names they enjoy learning to pronounce and quiz who can answer increasingly intrusive questions, and they get to tell stories about all that around the hypoallergenic environmentally friendly water cooler the next day.
Okay, so liberals like diversity and multiculturalism, but why should they value it?
In fact, a study of history indicates that multiculturalism is valuable on its face. Though he doesn't call it such, Jared Diamond describes a version of it in Guns, Germs, and Steel when he posits a hypothesis to explain why Europe conquered China and not the other way around. Simply put, Europe's many internal borders promoted factionalism and strife, but also allowed for the development of large countries and communications between them, whereas China was large and monolithic. This is simplistic, not least because China was exposed to outside influences and conquered multiple times. However, I believe it's true at its core, because China always viewed itself as the center of the world and even those who conquered it tended to agree (just as 'Mediterranean' means "middle of the world", so does 'Zhongguo' mean something similar).
China has a long history of inquisitively exploring, inventing powerful new technology (printing, firearms, explosives), developing them a little bit, and then completely abandoning them. Contrarily, Europe enthusiastically adopted these new technologies and even when conservative forces attempted to suppress them, those conservative forces were wiped out either by opponents who understood the power of the new technology within the state or by opponents who successfully used it against them from without. In other words, Europe was for centuries aroil with conflict that tested, improved, and discarded technologies, philosophies, cultures, tactics, etc. This is a controversial style of argument because it stinks of group selection, which notion evolutionary biology has been tussling over for decades*.
Compare this to suggestion that among the contributing factors to the American Revolution and the society/government that sprang out of it was the syncretism of European schools of thought with the much more egalitarian cultures of the Native Americans. That is to say, the American nation is something new, a combination of those two very different cultures. And then throw African cultures into the mix, and is it any wonder that rock and roll took the world by storm?
In the end, that's my argument for multiculturalism, diversity. Recall that our grandparents grew up with an entirely different variety of banana. Bananas, in their current form, are a wholly artificial human construct, a seedless clone race grown only for our consumption. That's why, when a disease struck, it virtually wiped out the Gros Michel (Big Mike) cultivar, which was replaced by the current banana, the Cavendish. In the same vein, were our culture to lack diversity, then should some virus of the mind or technological development come along that was incompatible, we could be wiped out.
One of the costs of maintaining diversity is that it makes it difficult to function. Some subcultures here in the US are like an autoimmune disorder, attempting to eliminate what they see as hostile, invading aliens, but which are in fact healthy growths. Others, like theocratic fundamentalist Christians, are potentially deadly cancers (their less active fundamentalist brethren are more like benign tumors. Not actively deadly, but they bear watching). Deviating from the biological metaphors for a bit, the fact is that multiculturalism is actually just more difficult to live with. We are all more comfortable when we're around people like ourselves, and our stress levels go up and sense of community goes down when surrounded by people not like ourselves. A diverse community is, in a very real and very unfortunate way, a less happy and stable community.
Those are the trade-offs. On the one hand, being open to new cultures and ideas has exposed us to the humanity of different peoples, helping to bring about the human rights revolution, feminism, civil rights; a truly healthy, vibrant society. On the other hand it can occasionally be stressful.
Suck on that, conservatives.
* Given that certain behaviors make sense only in the context of a group consisting mostly of members that also exhibit those behaviors (think cooperation, loyalty), I don't think group selection can be ignored, however I would consider it a secondary effect most of the time, as even in the context of the group, the individual has to compete with other individuals of the species to reproduce.