I believe the nature of intelligence is the ability to understand and use the nature of the information precived. The criteria should be some combination of analytical skills, thinking speed, memory, and perception. By analyzing, I mean deductive reasoning, inductive reasoning and the overall ability to wield logic. Given a scenario, how many conclusions, possibilities, or patterns can you draw from it. I have seen people capable of memorizing capitals of countries/states, country locations, all the presidents, peoples names and so forth but can't figure out how things work together, or be able to use all this information to solve simple problems.
Thinking speed is important as well (It's a problem of mine). You may be able to analyses but it may take you a long time to do so. I have a friend who can solve simple math problems and read at light speed but when it comes to learning new concepts he's very slow. Often times he will need directions repeated to him, and he'll need an example of a relation between the concept concept to something that he's familiar with and works in a similar way.
I believe a good memory is not only how much information you can retain, but for how long you retain it for. Perception is the ability to sense, observe and simply pay attention to your surroundings using your five senses. and can be measured in how much you can perceive in what amount of time. Someone with great powers of observation can be shown a picture of a building for a second and he'll tell you everything he saw such as ?number of windows, number of floors, number of cars, model and colors of the cars, parking lot size, and number of trees in the background.? Someone like me would have to look at it for a bit longer in order to ?notice? the same amount of information the other guy did.
Intelligence is a system that uses these traits together. You perceive information, remember it, then use it to conclude new information and understand the nature of what you have just precived. How smart you are could be expressed in how many inferences you can make in a rate of time.