There are basically 2 ways an estate can devolve to the heirs, either 'per capita' or 'per stirpes'. Imagine the deceased has had 3 children, 2 of whom survive him. The 3rd dies before the testator, but leaves 2 children. Under per capita ('by headcount') devolution, the estate is divided 4 ways - equal shares to the 2 children AND the 2 surviving grandchildren. Under 'per stirpes' devolution ('by branches'), the estate is initially divided 3 ways; the surviving children get a third each and the 2 grandchildren, representing their (pre-)deceased parent, get one sixth each. Per stirpes is often regarded as fairer, certainly by children who would otherwise have their share reduced significantly, depending on the number of surviving grandchildren of a predeceased sibling! This explanation is a bit complicated, but so is the concept. I hope it's clear enough.

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Note added at 19 hrs (2009-05-11 11:51:55 GMT)
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See also http://www.interinheritance.co.uk/glossary/p/per-stirpes.htm... or the wikipedia article, which contains reasonably good definitions and diagrams, at http://en.wikipedia.org/wiki/Per_stirpes. Not at all confined to intestacy cases.