This is a form of statistical analysis used for multivariate data that is Normal distribution. It is quite robust, in the sense that even if the data is not completely Normal, the results are fairly reliable. You might use this, for example, if you have performed an experiment measuring response times with several users, each performing several tasks with two alternative interactive systems; in this case you have three variables: user x task x system. You are probably interested in which system is better overall, but the different tasks may vary in difficulty and the users may differ in expertise. The ANOVA can disentangle these effects, giving you main effects: averages for each user, task and system; as well as interaction effects such as whether some tasks are better suited to one system or the other.
Used on pages 48, 52, 121, 122
Also known as analysis of variance