Imagination is one of those concepts, like teamwork and persistence, that get put on posters to try to inspire white collar workers doing menial tasks to like their job better, and to give the illusion that they have some important creative role in the company.
This might give one reason to think that the concept is kind of fluffy and impossible to study. Well, it is kind of fluffy, like many concepts (ever try to define "chair?"), but it does indeed get studied, by no fewer than three separate disciplines: psychology, philosophy, and computer science.
Broadly speaking, psychologists study the effect of imagination on the mind and behavior, as well as what kinds of things people are capable of imagining. I'll give a few examples of each.
It has been found, for example, that imagination can help hand and leg performance in stroke patients who have suffered some weakening on one side of the body (Dickstein & Deutsch, 2001). Imagining doing sports often makes one better at doing the sport, just like real practice. This was even found for weightlifting (Yue & Cole, 1992)!
Imagining a make-believe childhood experience can make people actualy believe it happened to them (Garry, Manning, Loftus & Sherman, 1996), and indeed all episodic memory recollection, even though it doesn't feel like it, is partially a reconstruction based on imagination (Schacter & Addis, 2007).
The other thing psychology focuses on is what is called visual mental imagery, which is when you picture something in your head so clearly that you can "see" it in your mind's eye. Psychologists study what kinds of information is available in these imaginings, and how they can be manipulated. For example, it has been found that the farther an imagined object needs to be rotated in the mind, the longer it takes for it to happen (Shepard & Metzler, 1971).
Readers interested in the psychology of the imagination can look at (Markman, Klein, & Suhr, 2009).
Whereas psychologists' methodology focuses on measuring and analyzing the behavior of people in specific situations, philosophers focus on known facts and reason with them to try to come to new understandings. In practice, this means that they focus on completely different questions. I'll give an example of just one.
Imagine that an elephant started running down a busy city street. Most of my readers would probably also imagine that people would run away, and be startled. What you're doing in this case is using what you know about the real world to influence your imagination. We do this all the time, particularly when reading stories. Now, if you saw an actual elephant running down the street, and were asked to predict what would happen, you'd probably also predict that people would run away and be startled.
This example demonstrates that we reason with imagined truths much like actual ones. Philosophers call this the "common code." So far so good?
The problem is this: if we reason with true things and imagined things with the same cognitive processes, how is it that we don't actually believe the things we imagine? For example, if I told you to imagine that you could breathe underwater, what stops you from trying to the next time you take a swim? How does your mind keep your imaginings from contaminating your beliefs about reality? There are several ideas out there, but the debate about the answer is still on-going. There is not yet a cure for the common code.
Readers interested in the philosophy of the imagination are invited to read (Nichols, 2006).
There are a bunch of people in graphics and artificial intelligence research that are trying to make computers be able to imagine things on their own. They don't call it imagination, but rather use terms like procedural generation, and synthesis.
There is a need to have computer create novel yet realistic graphics and sound. For example, if you use a search and rescue training simulation over and over again, you learn less and less from it, because you get used to what is in it, much like playing the same level again and again on a video game. If the computer can create new scenarios automatically, then the training can be more effective.
There is a need for this in entertainment, too. Movies need computer-generated extras, and computer games need buildings, and trees. It's prohibitively expensive to have human designers create every bit of an environment.
Here is a video of a procedurally-generated city: http://youtu.be/-d2-PtK4F6Y
It's still primitive, but some games already use procedural generation. Diablo, for example, uses computer-generated dungeon maps. Arguably, this is a primitive form of computer imagination. Yes, the rules were programmed by people, but often when we imagine things we use constraints that we learn. For example, we are unlikely to imagine the planet Saturn in a bedroom that we want to be realistic.
You can play a procedurally-generated game: Infinite Mario Bros., a clone of Super Mario Bros. that endlessly creates new obstacles for you.
A great deal of procedural generation has to do with creating seamless and realistic textures-- for example skin, or brick, or grass. Some make buildings, others landscape, or trees, or faces.
There is barely any communication between the disciplines, and very few people are trying to bridge those gaps. The philosophers cite the psychologists, but that's about where it ends.
For such an interesting and important field, it's a shame. There isn't even a book out that describes how these different findings relate to each other.
...Yet. I need to get writing.
Pictured: A procedurally-generated planet from http://calculatedimages.blogspot.ca/2010/09/procedural-planets.html
Dickstein, R., & Deutsch, J. E. (2001). Motor imagery in physical therapy practice. Physical Therapy, 87, 942-953.
Garry, M., Manning, C. G., Loftus, E. F., & Sherman, S. J. (1996). Revelation without presentation: Counterfeit study list yields robust revelation effect. Memory and Cognition, 27, 339-343.
Markman, K. D., Klein, W. M. P., & Suhr, J. A. (Eds.). (2009). Handbook of imagination and mental simulation. New York, NY: Taylor & Francis Group.
S. Nichols (ed.) (2006). The Architecture of the Imagination. Oxford: Oxford University Press.
Schacter, D. L., & Addis, D. R. (2007). The cognitive neuroscience of constructive memory: Remembering the past and imagining the future. Philosophical Transactions of the Royal Society of London: B, 362, 773-786.
Shepard, R and Metzler. J. "Mental rotation of three dimensional objects." Science 1971. 171(972):701-3.
Yue, G. H., & Cole, K. J. (1992). Strength increases from the motor program: Comparison of training with maximal voluntary and imagined muscle contractions. Journal of Neurophysiology, 67, 1114-1123.