I actually follow Howard Gardner's theory of the Seven Types of Intelligence. He basically states that there are different kinds of "smart," which explains why some people are good at some things, while they lack in other areas that other people might do well in. The seven kinds are:
1. Linguistic ~ People who are linguistic, or word smart, tend to do well with languages and with words. They like writing and reading, etc.
2. Logical ~ People who are logical, or number smart, are good with puzzles and problem solving. This is the kind of smart that people who excel in math are.
3. Kinesthetic ~ Also "body smart," I think. These people are good at sports, or physical activies like dancing. (This one is also definitely not me, rofl.) These people often learn best by doing things for themselves, I think.
4. Spatial ~ Also visual or picture learners, these are the artists. ^^; They think through images and they're often very good at visual arts, such as drawing sculpting, etc.
5. Musical ~ People who are musical (I think it's also called aural, but I can't remember) learners are good at picking up sounds or recalling tunes. They listen well. I don't remember much else. XD
6. Interpersonal ~ People smart! These are the leaders in society; they're good at communicating and can understand other people with ease. They're good at getting people to interact with each other and whatnot. ^^;
7. Personal ~ Last but not least is self smart. These people aren't necessarily introverts, but they can identify with themselves easily and they know themselves inside out. Often times, though, these people tend to be shy.
So... yeah. I use the above to define smart... though I suppose I tend to lean more towards defining smart mostly as logically smart, eheh. ^^;; I'm not the greatest to be thinking about these things since whenever I take tests to see which smart I fall under, I end up with high scores in all of them since I like learning in a bunch of different ways. XD;