The concept of ANOVA can be confusing in several aspects. To start with, its name is an acronym for "ANalysis Of VAriance", but it is not used for analyzing Variances. (F and Chi-square tests are used for that.) ANOVA is used for analyzing Means. The internal calculations that it uses to do so involve analyzing Variances -- hence the name.
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.