Imagine using a highlighter to draw a band to cover as most of the points in your scatterplot.
Most points in the scatter graph can be covered with a straight band.
Most points in the scatter graph cannot be covered with a straight band (or the band is curved).
I notice that most of the points in my scatter graph lie in a straight band.
This means that the relationship between Variable 1 and Variable 2 is linear.
I notice that most of the points in my scatter graph do not lie in a straight band.
This means that the relationship between Variable 1 and Variable 2 is non-linear.