Problem representation relates to the fact that how we see or conceptualize a problem defines how we try to solve it. Solving difficult, high-impact problems requires finding a representation of the problem that is solvable. If you are not able to solve the problem that has been presented to you, the answer may be to simply change the problem to one that you can actually solve. In that way problem representation can hold the key to valuable innovation.
Most people who want to transport a gallon a water from one place to another look for a solution by hunting for a vessel like a jar or a bucket. Their representation of the problem is based on the belief that you need to contain the water in order to move it. But someone else may do the opposite and free the water by converting it to steam. Then they can move it through the air. Meanwhile any person may solve the same problem by simply freezing the gallon the water and then carrying it as a block of ice without the need for steam or a vessel. So the potential solution all depends on the particular problem representation vision.