Linear:
This scatter plot forms a straight line. The points are rising from left to right across the graph in a linear manner.
A line can be drawn with approximately the same number of dots above and below the line.

Obviously nonLinear:
This scatter plot clearly does not form a straight line. First the dots go up, but then they turn and go back down.
While a "line" of best fit is not possible with this scatter plot, it may be possible to draw a "curve" of best fit. 
Not Obviously nonLinear:
It is not easy to determine whether this scatter plot is linear or not, but it is nonlinear. See *Hint below.
A curve can be fitted to this data with approximately the same number of dots above and below the curve. 