According to brain scientists, the part of the brain that gives us imagination is the very same part that gives us memory. Essentially, it is our ability to shuttle back and forth in time that we perceive as memory. In point of fact, most of us spend very little time in the present, and are almost always living somewhere in some future anticipatory curve. Indeed, one major aspect of (visual) intelligence is the ability to push this curve into the future, but there appears to be some trade-off in memory in doing so.
I agree with @SeventhSense that imagination is where we experience the internal dialogues we normally regard as “thinking.” However, I think that intuition and lateral thinking are different processes insofar as they are almost instantaneous. Creativity is the ability to juxtapose two different frames of reference, such as the idea of a Volkswagen beetle being likened to a pregnant lady. As with memory, imagination is highly selective and prone to salience effects, so that if you buy a Volkswagen, you tend to notice Volkswagens everywhere you go. This is important because, these images later become consolidated into useful information during sleep, as the useful potential of memories is explored by running dream scenarios under relaxed conditions that allow the mind to take full advantage of its ability to juxtapose interpretive frames. In this respect, learning and deep problem-solving shift into high gear in sleep. And it is a lesser analogue of this that we experience in creative day dreaming.
As @wundayatta points out, there is always a layer of imagination between us and the “real” world. For some that layer is thicker than others, creating a sense of unreality in some, but also creating an engaging world of innovation and artistic possibility in others. It is in this event horizon of imagination that our defense mechanisms determine what we pay attention to and what we ignore, leading some of us to see the glass half empty or Obama as a Bolshevik.