As I understand it, multiculturalism is the idea that multiple different cultural traditions should be allowed to coexist and perpetuate themselves inside a single society or country. As some people in this thread have pointed out, it is in opposition with the melting pot approach to diversity, where immigrants to a country influence the substratum with their own cultural particularity, but at the same time are expected to assimilate to this substratum culture.
Of course, there is no such thing as “pure” multiculturalism in the real world. Immigration countries put into place multicultural policies (these can be many things, from the general, such as mandating cultural diversity teaching in schools, to the specific, such as accommodating minorities’ cultural or religious needs even as they conflict with the laws in place or offering services to residents in many different languages, with everything inbetween) in order to be attractive places for immigrants and because they simply cannot ignore the cultural diversity that actually exists on the ground. But at the same time, they expect all citizens to fulfill their part of the social contract. They would demonstrate this, for example, by expecting people to respect the law of the land, even if it may be different from the one in their country of origin, and to be able to communicate in the national language (at least eventually).
What it usually means when someone says that multiculturalism has failed is that they believe the government should put more emphasis on integration than on maintaining diversity. Both are important parts of immigration policies, but when people start to have trouble recognizing their society (i.e. the substratum is changing too fast) they believe someone should step on the brakes. It’s really that they believe their country should be somewhere else on the continuum, rather than an indictment of the ideology of multiculturalism as a whole. Well, except for Arcite who seems to believe that ending all immigration is necessary.