Key difference: The independent variable is the one that just happens; it does not rely on anything else, whereas the dependent variable is usually dependent on the independent variable.

Independent and dependent are two terms that are actually antonyms. Essentially, that means that they are opposites.

Dictionary.com defines Independent as:

• Not influenced or controlled by others in matters of opinion, conduct, etc.; thinking or acting for oneself: an independent thinker.
• Not subject to another's authority or jurisdiction; autonomous; free: an independent businessman.
• Not influenced by the thought or action of others: independent research.
• Not dependent; not depending or contingent upon something else for existence, operation, etc.
• Not relying on another or others for aid or support.
• Rejecting others' aid or support; refusing to be under obligation to others.
• Possessing a competency: to be financially independent.
• Sufficient to support a person without his having to work: an independent income.
• Executed or originating outside a given unit, agency, business, etc.; external: an independent inquiry.
• Working for oneself or for a small, privately owned business.
• Expressive of a spirit of independence; self-confident; unconstrained: a free and independent citizen.

Whereas, Dependent is defined as:

• Relying on someone or something else for aid, support, etc.
• Conditioned or determined by something else; contingent: Our trip is dependent on the weather.
• Subordinate; subject: a dependent territory.

Essentially, independent is when one does not have to rely on something or somebody, It is when they only rely on themselves. Dependent, on the other hand, is when someone does have to rely on somebody else. They may not be able to get by without whatever or whoever they are dependent on.

In experiments or mathematical modelling, variables are used. Variables are essentially anything that plays a factor in the experiment or modeling. For example, if we were conducting an experiment to see the relation between sunlight and growth of plants; sunlight and the growth of plants would be the variables.

Variables can be divided into three types: independent variable, dependent variable, and other. Essentially, the independent variable is the one that just happens; it does not rely on anything else, whereas the dependent variable is usually dependent on the independent variable. It performance or instance of happening relies on the presence of the independent variable.

Let us look at the example again: In the experiment to see the relation between sunlight and growth of plants; sunlight just exists. It does not rely on the growth of the plants, hence, in this experiment, sunlight is the independent variable. The growth of the plants does rely on the presence of sunlight; if there would be no sunlight, plants would not grow. Hence, the growth of the plants is the dependent variable, because it is dependent on the amount of sunlight present.

In a graph, the independent variable is always graphed on the x-axis (horizontal, bottom one); whereas, the dependent variable is groups on the y-axis (vertical, side one). This is mainly because the value plotted on the y-axis, always corresponds to the x-axis. The x-axis is always independent of the y-axis.

Image Courtesy: arose.iweb.bsu.edu, docstoc.com