Draw two overlapping circles to represent the shared variance between A (the treatment or group membership variable) and Y (the outcome variable). Now draw three overlapping circles to represent the shared variance among Y (a quantitative outcome variable), X (a quantitative covariate), and A (a group membership variable).
Use different versions of these diagrams to illustrate that the effect of including the covariate can be primarily to reduce the SSerror, or primarily to reduce SSA.