It’s basically a framework that makes it much easier to develop and install system hacks (usually GUI hacks, like ShapeShifter).
I asked Omnis that question, because although the current version of APE is perfectly safe, older versions (<2.0.2) will cause a Leopard installation to fail. That in itself isn’t so bad, since someone who is willingly installing APE should know what they’re getting into and should be upgrading regularly (I personally use APE, BTW – hasn’t given me any problems in nearly five years). The big, big problem that has been leading to a lot of botched Leopard installations is that the smarties at Logitech decided some time ago to use APE for their Logitech Control Center (the mouse drivers they use for Mac OS). I can’t put into words how stupid that is – no consumer should expect that installing mouse drivers will install a potentially dangerous system hack framework. The folks at Unsanity aren’t totally in the clear themselves, because APE requires installation in a system folder that Apple explicitly warns against, but Logitech really deserves the blame IMO. That’s such a poor decision on their part.