Three or Multi-Dimensional Situations (Log-Linear)
We have done analyses with A X B tables, such as Gender vs. Car Type.

Maybe you are also interested in Gender, Profession, and Car Type. This would be an A X B X C situation. Is car preference separate from Gender? Is it independent of Profession? Maybe the pattern of differences for the Genders depends on the Profession (doctors are like X and lawyers are like Y). This would be an interaction as in factorial ANOVA.

You can analyze the independence of 3 or more categorical variables with a procedure called Log-Linear analyses.