Graphically, interactions can be seen as non-parallel lines connecting means when we are working with the simple two-factor factorial with 2 levels of each main effect (adapted from Zar, H. Biostatistical Analysis, 5th Ed., 1999). Remember interactions are referring to the failure of a response variable to one factor to be the same at different levels of another factor. So when lines are parallel the response is the same. In the plots below you will see parallel lines as a consistent feature in all of the plots with no interaction. In plots depicting interactions, you notice that the lines cross (or would cross if the lines kept going).