It would be useful to add an interaction term to the model if we wanted to test the hypothesis that the relationship between the amount of bacteria in the soil on the height of the shrub was different in full sun than in partial sun.
One possibility is that in full sun plants with more bacteria in the soil tend to be taller. But in partial sun plants with more bacteria in the soil are shorter.
Another is that plants with more bacteria in the soil tend to be taller in both full and partial sun. But the relationship is much more dramatic in full than in partial sun.
The presence of an interaction indicates that the effect of one predictor variable on the response variable is different at different values of the other predictor variable. Adding a term to the model in which the two predictor variables are multiplied tests this. The regression equation will look like this:
Height = B0 + B1*Bacteria + B2*Sun + B3*Bacteria*Sun
Adding an interaction term to a model drastically changes the interpretation of all the coefficients. Without an interaction term, we interpret B1 as the unique effect of Bacteria on Height.
But the interaction means that the effect of Bacteria on Height is different for different values of Sun. So the unique effect of Bacteria on Height is not limited to B1. It also depends on the values of B3 and Sun. The unique effect of Bacteria is represented by everything that is multiplied by Bacteria in the model: B1 + B3*Sun. B1 is now interpreted as the unique effect of Bacteria on Height only when Sun = 0.