Our brains are extremely complex and compiles vast amounts of information in various different regions. These regions are then separated into two "lobes". One side is primarily identified with emotion and creation. The other is generally identified with logical thinking and analysis. To help access certain regions of our brains, our eye movements are connected to certain processes. For example, looking up and right, accesses the part of your brain that constructs visual images.
When they look up and left, (their left) it accesses there memories. You will often see this when someone is describing a place they have been or retelling a story. It is also part of detecting a lie.
Looking up and right, accesses visual construction. You might see this when someone is trying to describe a place that they do not completely recall. It is also part of a lie! If someone begins to tell you something by looking up right and then looking up and left, they have moved a creation into a memory. Lies that are partially true are much harder to detect. Thus your brain moves the creation to a memory. (As a disclaimer, it is rare to find in a person, but some people are the opposite of the directions I have stated.)