An independent variable has a variety of meanings, depending on the discipline using the term. In science, for example, it is the variable that is being manipulated so that the change in another variable, referred to as the dependent variable, can be measured.
One of the biggest challenges many people have to deal with when looking at an independent variable is the fact that all variables depend on something. While that may be true, there is an easy way to determine what this variable is. Simply ask the question: What do I need to change in order to influence, or try to influence, another thing? The thing that needs changed would be your independent variable.
Another way to look at it is to understand that this variable is the one you can control. This is true for variables in both science and statistics. A dependent variable cannot be controlled, but can be influenced. For example, adding food coloring to a white carnation to change its color and see how pigmentation can be affected is an independent variable. How much the color is affected, if at all, would be the dependent variable. While you may be able to produce a different color of flower, the extent of the change, and how quickly it happens, are generally beyond the control of the experimenter.
There should be only one independent variable in any science experiment, at least at most levels of experimentation. For those who believe they have more than one of these factors, further thought should be done to truly understand what may be affecting the experiment. If more than one thing is possibly affecting the experiment, then it will be harder to pinpoint an exact cause. Therefore, it is best to keep experiments as controlled as possible, which means only having one independent variable.
In mathematics, the independent variable is one whose value does not depend on any other variables. For example, suppose you have the equation y=x+5. In this case "y" is the dependent variable and "x" is the independent one. This is because the value for "y" is dependent on the value of "x". In fact, the value of "y" cannot be determined without knowing the value of "x" because of that dependency. Once the value of the independent variable is provided, finding the value of the dependent variable becomes simple algebra.