ANOVA models are used to study the effects of the independent (predictor) variable(s) on the dependent (response variable), without making assumptions about the ``shape'' of the relationship. They are used in randomized experiments, where the assumption of random uncorrelated (and perhaps normal) errors in the regression model is carefully built into the data by the experimenter, and in observational studies, where the assumption of random uncorrelated (perhaps normal) errors must be argued into the problem.
Many of the ideas in this section were taken from Chapter 14 of