Analysis of Covariance. This is really a special case of multiple linear regression, used in ANOVA-like settings with some continuous covariates in addition to the categorical ones.
ANCOVA is used in ANOVA-like settings to control for any independent variable, which although not of interest, may affect the relationship between the dependent variable and other variables in the model. For example, to test the effect of asbestos on lung cancer, smoking would be included as a covariate.
ANCOVA is not substantively different from the General Linear Model: the term 'ANCOVA' may be used when a predictor of interest is categorical and it is wished to control for the effects of one or more continuous predictors; the sums of squares for the former are examined after partialing out those for the latter.