Aggression Factor, or AF, is a ratio (not a percentage) which describes the nature of a player's bets.
The formula for any given street is ( (bets + raises) / calls ) .
Bets, raises, and calls are all "money bets." Bets and raises, however, are aggressive (increasing the cost of playing) and calls are passive. Checks and folds are not in the equation because they are not bets.
An AF of 1.0 implies that the person makes bets about as often as they call bets.
Generally speaking, in Limit Hold'em, an AF dropping below .75 is to getting passive; many poor players online have AF's of .7 or lower. An AF over 1.5 or so is generally getting aggressive.
What does it mean to me?
Someone with a very low AF who bets or raises is very likely to have the strength they represent. You must respect their bet when deciding how to play your hand.
Someone with a very high AF is liable to be bluffing or semi-bluffing much of the time. You might call or raise back more liberally.
More to it than that
There's an important subtlelty to understand regarding AF vis-a-vis someone's looseness. Talking Limit Hold'em again, a rock who only sees the flop 15% of the time and folds the flop 50% of the time may produce an AF of 3.0 by merely betting legitimate hands. Because they are so tight, they nearly always have a pair or high cards when they come in. Consequently, the 3.0 AF doesn't actually suggest excessive aggression. The mere fact that they're on one of the few hands they didn't fold tells you they are holding strong cards; StraightforwardPlay will lead to a lot of bets and raises.
On the other hand, someone who sees the flop 75% of the time who has a 1.5 AF is ridiculously aggressive. Someone seeing almost every flop can't possibly be catching their cards that often, so a high AF tells you they must be bluffing and semi-bluffing, probably too often.
Someone's AF for a given street does not tell you how likely they are to bet. However, if they do put money up, it describes the kind of money. Bets made by a passive player are very likely to be legitimate. Bets made by a very aggressive player may also be bluffs, semi-bluffs, or marginal value bets.
Consider someone who bets 25% of the time, raises 15 % of the time, and calls 10% (the rest of the time they check or fold.) Their AF is 4.0. ((25+15)/10)
Compare to someone who bets 35% of the time, raises 20% of the time, and calls 30% of the time. Their AF is 1.833. ((35+20)/30)
The second person is a lot more likely to bet or raise -- they do it 55% of the time, far more than the first player's 40% of the time -- yet their AF is lower, because they call so much more loosely -- three time as often!
Generally speaking, you should adjust your perception of their AF based on how often they fold up to that point. If they fold a lot, that high AF doesn't mean they are they are all that aggressive, and if they rarely fold, a low AF may not mean every bet is legitimate.
The weakness of the Aggression Factor as an indicator
AF's "Achilles' heel" comes from the fact that it is an attempt to roll a lot of behavior into a single number. It weights bets and raises against calls. It is an excellent single-number indicator which lets you describe someone's aggression. . . but it is not perfect. If you can move beyond single-number descriptions, you can do better.
If you know the call rate and the AF, you can tell if that low AF is because of too few bets, or too many calls -- you play against each of those differently. Or, let's say someone has a healthy-looking flop AF of 2.5 on a VP$IP of 18%, but you notice that they fold 80% on the flop. The healthy AF is reflecting the way they play when they stay in, but they clearly are too weak-chinned and fold too many flops regardless.
Several people are floating replacement factors for the AF, but any single-number factor will always suffer from being a single-number factor. Like everything else in poker, the best decision comes from knowing all the context, because ContextRules.
What about YOUR AF?
Most good players suggest that a good limit player's AF will tend to be above 2.0; some advise 3.0. The best advice is that once your aggression is over 1.5, do not try to to raise it merely for the sake of raising it. If you do, you may end up exercising DumbAggression. You either need to add aggression at the right times, or to reduce your bad calls. You need to know which is which, and to adjust your play accordingly. If your problem is calling to much, adding wanton aggression will not solve your calling problem! If you study when to avoid bad calls, and study when to add appropriate aggression, your AF will rise and so will your profitability. If you just slam, slam, slam the pot, your AF will rise, but your variance will skyrocket as your bankroll plummets!