Political-science jargon for a major split in a given society; the most common cleavages are ethnic, religious and economic.
Multiple cleavages in one society can be either "cross-cutting" or "reinforcing," which are assessments of the degree to which the multiple cleavages are congruent. That's best explained with an example: if you've got a society where some people are green and some people are blue, that's one cleavage. And then if some people are rich and some people are poor, that's another cleavage. If most of the green people are rich and most of the blue people are poor, you've got a reinforcing cleavage. If roughly equal numbers of each ethnic group are in each economic category, you've got a cross-cutting cleavage.
In general, cross-cutting cleavages contribute to social stability, while reinforcing cleavages are bad news. Combine a serious class divide with stark racial or religious differences and you've got the most basic components of a civil war starter kit. On the other hand, if the class divide cuts across the ethnic division, even the most committed demagogue would have difficulty whipping people up into a froth.
Cross-cutting cleavages tend to lead to political cultures of coalition-building and compromise; the United States is a fine example of this at its federal level, with its nearly non-existent party discipline and bills frequently being co-sponsored by Republicans and Democrats.
Reinforcing cleavages, even in healthy democracies, lead to much more competitive politics where every election necessarily means one social group wins at the expense of the other or others. In Quebec, Canada, each election is a contest between the nationalist, ardently pro-francophone, broadly socialist Parti québécois and the federalist, more anglophone-sympathetic, broadly market-friendly Liberal Party.
In extreme cases, too many cleavages in a given society can lead to an atomized political culture that is only barely functional. Italy, with its dozens of different governing coalitions since the Second World War is one pretty good example. Israel, though it's much more functional in terms purely of its electoral politics, illustrates the point with a less extreme case, with its multiple parties founded variously on economic ideology, religious conviction, and positions on the peace process.