ANOVA stands for ANalysis Of VAriance, a statistical model and set of procedures for comparing multiple group means. The independent variables in an ANOVA model are categorical, but an ANOVA table can be used to test continuous variables as well.
Although ANOVA stands for ANalysis Of VAriance, it is about comparing means of data from different groups. It is part of the general linear model which also includes linear regression and ANCOVA. In matrix algebra form, all three are:
$Y = XB + e$
Where $Y$ is a vector of values for the dependent variable (these must be numeric), $X$ is a matrix of values for the independent variables and $e$ is error.
The chief difference among ANOVA, ANCOVA and linear regression is that they arose in different fields. Also, ANOVA is usually restricted to cases where the independent variables are categorical, ANCOVA where some are numeric but most categorical. Regression (through dummy variables) can handle any type of independent variable.