A variable is the factor that changes in a controlled experiment.
The purpose of almost any experiment should be (or usually is) to determine if there is a relationship between two things, and if so, how that relationship works. Most professional research will often split these into separate experiments in order to minimize the possibility of causes and effects being confused. Much of the research involved in an experiment should revolve around determining what the variables are, and how to manipulate them.
The baseline, "textbook" method involves setting up two identical experiments, with only a single factor being changed between them. A different outcome might indicate that the variable is responsible.
In reality it's very difficult to replicate the kind of textbook one-variable experiment, wherein only one thing changes and produces only one kind of easily measured effect. It's especially difficult with humans, since there are so many variables that are impossible to account for. It's also important to consider how we're evaluating and interpreting the variable; for example, if I raise the temperature of a sheet of paper, and it doesn't catch fire, I can't conclude that paper cannot catch fire.
I can only conclude that the temperatures to which the paper was subjected did not result in fire. While this might seem obvious to us because the example is so familiar, this kind of jumping to conclusions and effects seems to happen all the time; for example, in diet research and publicity, where it is sometimes advertised that sugar leads to obesity, or that cell phones have no adverse health effects.