Ok there are a few things that happen over the boil:
#1: Water evaporates. We start with x volume of wort in the BK, after a period of time we have less than x volume because the water evaporates. This reduces overall volume and increases gravity (water evaporates, the sugar doesn't).
#2: Hops are utilized. If you take wort (all other variables equal), throw in an oz of hops and boil it for 15 minutes then done, it will be less bitter than that same wort boiled for an hour (or more). The longer the hops are in the boil, the more IBUs they contribute.
#3: DMS is boiled off, 60 minutes seems to be the industry-standard magic number for making DMS (DMS badddd, baddddd DMS) disappear. Longer won't hurt, it just won't help. Shorter boil times would hurt.
#4: Caramelization and malliard reactions. I don't know what these things mean, someone else touch base here.
Alot of higher gravity beers (barleywines and imperial stouts, for example) have a longer boil time because you will need to mash thinner and sparge more to get a good extract efficiency from such a large grain bill. Therefor, to get down to your necessary batch size you will have to boil longer. Also, these beers typically require more IBUs to balance out the large grain bill.
Hows that for a start to your boil time research
Someone else fill in the blanks!