The ANOVA (Analysis Of Variance) is a test to determine whether some detectable difference between two or more groups is more likely due to chance than to to "natural variation". Or (equivalently) it can be used as a guide to determining whether there is a certain level of confidence that one particular factor or factors are the more likely cause of some observed difference.
In the most basic sense the ANOVA tests hypothesis in the same way as Student's T-test for differences between means but allows for more than two independant groups.
The probability information produced by ANOVA is the F Ratio (named for Fisher).
Data for ANOVA can be from any number of data sets and there is no requirement that they be of equal size.
Let us consider an example.