If you collect a set of scores from people they will not all be the same. That is, there will be variance in the scores. Imagine you have three groups of people and each person provides a score on a test. There will be two sources of variance: (1) Some groups, on average, perform better than others and (2) the people within each group won't all perform at exactly the same level.

ANOVA allows us to look at these two types of variance in relation to each other. The first type is called EFFECT VARIANCE. It is the extent to which the scores are different from each other because some of the people come from a different group to the others, and this is what we are interested in. The second type of variance is called ERROR VARIANCE. It is not really interesting to us, as we would expect the people within a group to perform at slightly different levels from each other. What ANOVA does is to calculate the ratio (F-ratio) of effect variance to error variance (F = effect / error). If F is big, this means that the scores we measured differ from each other primarily because some groups are better than others, and this is interesting. If F is small, this means that the scores we obtained differ from each other primarily because there is a lot of random variation between the people we tested; a lot of noise, in other words.

It's done with Analyse > Compare means > One-way ANOVA