One way to "know" something is to memorize it—have it in your mind. I think this could be the shallowest form of knowing something, because it doesn't necessarily stay and it doesn't have to be very deep or understood to be considered memorized (interesting--understanding isn't the same as knowledge). This is the type of knowledge my professors have referred to as "regurgitated" knowledge—there isn't a change from going in to coming out.
Another level of knowing something is seeing how it connects to other things. Like knowing that hamburger was once a cow, or knowing that heroes are important to people because there's a form of hero in all the cultures you've looked into. There is a change in this one—you add contexts to the information, thus influencing how it will be interpreted (by you or by others) in the future.
Another level of knowing is understanding why, or at least realizing there is more going on behind the scenes. Understanding is knowing that a light switch works because the circuit has electricity running through it and a light bulb is part of the circuit. Understanding can also come in the form of not getting mad at your friend even though he's being a jerk, because you realize there is probably something going on below the surface, even if he won't tell you what it is.
|Found on Flickr.com Djumbo, creative commons license|