One use of this phrase is to assert one's dominance; aggressively in a situation. My favorite way it is used is to express one's desire to take their own direction, foregoing the direction of the crowd. The free-thinkers that drive the world.

A quote I love, written by Robert Siltanen for the launch of Apple's "Think Differently" campaign, is to me, a well-written example of the spirit of the phrase.

“Here's to the crazy ones. The misfits. The rebels. The troublemakers. The round pegs in the square holes. The ones who see things differently. They're not fond of rules. And they have no respect for the status quo. You can quote them, disagree with them, glorify or vilify them. About the only thing you can't do is ignore them. Because they change things. They push the human race forward. And while some may see them as the crazy ones, we see genius. Because the people who are crazy enough to think they can change the world, are the ones who do.”