In politics, centrism usually refers to the political ideal of promoting moderate policies which land in the middle ground between different political extremes. Most commonly, this is visualized as part of the one-dimensional political spectrum of Left-Right politics, with centrism landing in the middle between left-wing politics and right-wing politics. However, there is arguably more than one dimension to politics, so even the center has its own radicals as exemplified by radical centrist politics.
Centrists, with their fondness for majority rule, share some ideals with classical democrats, though they distance themselves from the strong ideological commitments often associated with that viewpoint. Close and sometimes overlapping with centrism are the ideals of political liberalism (in the European sense), though this philosophy generally emphasizes the individual at the expense of the community, while centrists seek a balance between the two.
Centrism is important because it applies to very large swaths of the populace. In many countries, most members of the public tend to identify themselves as independent rather than as left_wing, right_wing, or any other political wing. Politicians of many parties try to appeal to this so-called Vital Center, although many pundits find fault in this approach. For example, candidates using centrist politics to gain wider appeal risk losing support from the more idealistic members of their political parties. Also, centrist candidates may find themselves strongly agreeing with opponents in debates, potentially confusing voters as to how they stack up. This may have contributed to the controversial outcome of the 2000 U.S. presidential election in the United States (admittedly aggravated by political polarization among voters, a fairly different phenomenon).
Centrism in the Marxist movement
"Centrism" has a specific meaning within the Marxist political movement. It usually reflects an ideologically held position between a revolutionary and reformist position. For instance, the Independent Labour Party was seen as revolutionary centrist because they were a radical formation moving towards a revolutionary position and had the potential to become a full fledged revolutionary party or at least have a large number of their members move towards an openly revolutionary position. Marxist Centrism is often opportunistic, since it argues for a revolution at some point in the future but urges reformist practices in the mean time.
On a related note, the term "Centrism" also denotes positions held by some of the Bolsheviks during the 1920s. In this context, "Centrism" refers to a position between the Right Opposition (which supported the New Economic Policy and friendly relations with capitalist countries) and the Left Opposition (which supported a planned economy and world revolution). By the end of the 1920s, all three factions had been outmaneuvered by Joseph Stalin who, while casually aligning with each of them in turn, built his own power bloc and had the leaders of the three factions removed from their positions, imprisoned and eventually executed during the Great Purge. At the same time, he implemented policies that drew some ideas from each of the factions, combined with his own characteristic ruthlessness.
See: Two Articles on Centrism by Leon Trotsky (http://www.marxists.org/archive/trotsky/works/1934/1934-centrism.htm)