The purpose of bonus types is to give some logic to what things stack and what things dont.
Back in 2ED, somethings worked together, some things didn't and it was rarely clear which did, which didn't and even less clear why.
Player: I put on my ring that gives me a +1 to AC
DM: um, you can't put that on because you're wearing magical armor
Player: oh...
All: *sit there trying to figure out how a magical ring has anything to do with magical armor*
WoTC: *adds types to bonus' in 3ED to (mostly) prevent the above situation from happening*
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Basic premise: You can only have a single bonus of a given type in effect simultaneously (i.e. 2 bonus' of the same type don't stack. They can be in effect at the same time, but you only receive the benefit of the highest value.)
This clears up the AC bonus confusion that I referenced in my example. The +1 AC ring, is a deflection modifier, +1 armor gives an armor modifier, so the character can recieve the benefit of both. However, if he had two +1 AC rings, he would not receive a +2 bonus to AC for wearing both. Bonus types give a logic to modifers that didn't exist before. Even if it still might not "totally" make sense that 2 rings doesn't protect more, at least there is a consistant logic to discern what stacks and what doesnt.
A competance bonus to any value is a pretty good type of bonus, usually one only granted by feats or class features (since a really nice sword (enhancement bonus to attacks) doesn't acctually make you more skilled at swordplay, though it does increase your effectiveness. Basically these feats grant competance bonus' because they stack with just about any other bonus you are likely to have (since no item gives a competance bonus.)
Exceptions: a small number of bonus types DO stack with other bonus' of the same type. I *think* the only two that do stack are Dodge and ... Circumstantial (since many circumstances in your favor can make your chances even better.)
-TV