ANOVA stands for Analysis of Variance.

The ANOVA is a statistical test used to compare the difference in means of two or more groups.  The test takes into consideration the variance of the sample data, the sample size, and the differences between the sample means.  Variance refers to how spread out the data is and how the data compares to the mean.  If there is a lot of variance within the groups being compared, there is a bigger chance that differences between the means is due to chance.  If sample size is large there is less chance of selecting outliers by chance, and if the differences between the means of samples is large it is more likely that the difference between the means of the populations represented by the samples is also large.  Using variance, sample size, and differences between sample means, the ANOVA is used to calculate the F value which is then used to determine the probability that differences between the means is statistically significant.

A One-Way ANOVA is used when there is one independent variable split into two or more mutually exclusive groups and one dependent variable.  A Two-Way ANOVA is used when there are two idependent variables, and a factorial ANOVA is used when there are more than two independent variables.