A linear pattern is when the points form a straight line. For example the following points follow a linear pattern: (0, 0), (1, 2), (2,4), (3,6). These points are all increasing by the same amount. X is increasing by 1 while Y increases by 2.
A non-linear pattern can pretty much be anything that doesn't follow an exact rule. Like: (0,1) (4,3), (6, 12), (7,9). These points would not form a straight line, it would just be a bunch of random points everywhere.
I hope that helps!