Hi Ariel,
The "one" and "two" refer to how many independent variables are included in the ANOVA. If it is a one-way ANOVA, there is just one independent variable. As an example, if you wanted to look at the effect of class (working class, middle class, and upper class) on life satisfaction, you would use a one-way ANOVA.
However, if you wanted to break up your groups by a second independent variable, you would have to run a two-way ANOVA (also referred to as factorial ANOVA). As an example, maybe you want to look at the effect of class (working class, middle class, and upper class) and sex (male, female) on life satisfaction. Using a factorial ANOVA also allows you to look at possible interactions between your independent variables (e.g., the interaction between class and sex on life satisfaction).
Hope this answer helps!
-Mike
