An effect is the result of something. It is an outcome, a result, a reaction, a change in Y brought about by a change in X.
An effect size refers to the magnitude of the result as it occurs, or would be found, in nature, or in a population. Although effects can be observed in the artificial setting of a laboratory or a sample, effect sizes exist in the real world.
When researchers estimate effect sizes by observing representative samples, they generate an effect size estimate. This estimate is usually expressed in the form of an effect size index.
For a good introduction to effect sizes – how to report them, how to interpret them – check out my book Effect Size Matters…