Suppose you have to explain linear regression to your granny. She is well educated, she knows even the idea of the hypothesis testing, but before you start to tell her what regression is she asks you: "Why do I need to study a regression? How could it help me?"
The problem is to explain the goals and benefits of a linear regression without mathematical terminology (without definition of linearity, for example). Can it be done?
My variant is "Suppose we have Y and X - vectors of equal length (continuous measurements). We want to study if Y has a relationship with X. Linear regression can help us to establish properties of one particular type of a relationship".