Characters always do something for a reason. Writers usually call that reason the “motivation.” I like to break that out into three main parts, and let me go backward from the most visible parts to the least visible parts:
1) A STORY GOAL — Each character should have only one of these and it should be a clear and objective goal. Your reader should know what it would look like for the character to reach her goal. Scarlett O’Hara wants Ashley Wilkes. Either she gets him to marry her, or she doesn’t. Either way, you can have no doubt. This part of a character’s motivation should be one-dimensional.
2) AN AMBITION — Each character has something abstract that they want out of life. Miss America wants “world peace.” But what does that look like? Ambitions are always fuzzy. They have to be; they’re abstract. Each character translates their ambition differently into a concrete story goal–which we talked about above. Scarlett wants to be “the belle of the ball forever.” And she believes that marrying Asley will give her that. She’s mistaken, but that’s OK. She believes it. That’s what drives her. This part of a character’s motivation should also be one-dimensional.
3) VALUES — Each character believes certain core truths to be self-evident. No proof is needed that these core truths are really true, because it’s “obvious”–at least to the character. The ambition we talked about above always springs from your character’s values. This is where you want your character to be multi-dimensional. You want your character to have several values–core truths–and these should be in conflict. Scarlett thinks it’s obvious that “nothing is more important than being the center of attention.” This drives her ambition to be the belle of the ball. But Scarlett also believes that “nothing is more important than surviving.” This leads her to do all sorts of things that some of her friends are just too genteel to do. Scarlett is willing to get her hands dirty doing things that no belle of the ball should ever do. Scarlett’s values are in deep, deep conflict, and that’s what makes her a three-dimensinoal character.
I’ve never heard it explained exactly like this, but I think Randy is absolutely correct.