When to use anova versus ancova?

Both methods may be expressed as Linear Model, the ANCOVA aiming at testing the relationship between two continuous variables accounting for the effect of an other categorical variable. You can think of it as a way to estimate the effect of one continuous variable (e.g. height) on a given outcome (e.g. weight), adjusting for a factor thought to modulate this relationship (e.g. gender). In other words, you could test the following hypothesis: Is height related to weight to the same extent in males and females? With ANOVA, on the contrary, only categorical variables (or factors) enter the model, and the response variable is continuous. So, the ANCOVA may be seen as a compromise between purely multiple linear regression and ANOVA, but it's all the same: An ANOVA may be viewed as a linear regression with a k-level factor recoded as k-1 dummy variables.

The following paper would probably help as a first start, Misunderstanding Analysis of Covariance.