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Interaction arises when effect of one factor, known as input variable, on the dependent variable, named as output variable, differs among levels of other factors.

Example would be a pain relief drug trial with two factors: drug dosage and gender. The dependent variable is pain and is measured on the scale of 0 to drug Mg.

It is observed that the average pain for male and females is same which is 20.  Although the drug had no effect on pain, the interaction between gender and dosage could be explained that the drug works for men and, caused pain in women.   If the interaction effect wasn’t considered then the drug dosage wouldn’t work.   If only gender was observed then there is no significant difference between men and women.

References

Langley, R. (n.d.). Practical Statistics Simply Explained.