http://stattrek.com/regression/residual-analysis.aspx?Tutorial=AP

The page contains the following:

"A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate."

I cant figure out why randomly dispersed points suggest a linear regression model is appropriate; and dispersped points in an ordered manner being inappropriate.

Can anyone elaborate, in layman terms, why this is the case??

Many thanks in advance