It's primarily used by the AI to determine the depth of its various internal search trees.
For example, a lot LOT of time is spent by the AI evaluating area threats. The intelligence factor helps determine the radius for those searches when it builds its threat matrix. You get into diminishing returns in a hurry (let's face it, if an enemy is 100 tiles away and moves at 2 tiles per turn, it's not really very worryable0. On the other hand, cities looking at potential threats that are 12 tiles away might be useful as opposed to cutting off looking at units that are further than say 2 tiles away).
That's just one example. There's lots of other things like that such as how often the AI should look at upgrading its units, how often it should evaluate the inventory of its champions, how often it should look at shopping.
Anything above 10 is likely to wreck performance and cause memory problems.
The AIFOWCheat is probably the most lethal setting. Letting the AI not worry about FOW will result in faster performance but it's also pretty obvious that the AI knows where everything is.