Skew lines are lines in space that do not lie in the same plane. Moreover, they are not parallel and they do not intersect.
In the figure below, the red line and the green line are skew lines.
Notice that the red line is not on the same plane as the green line. Notice also that they are not parallel and they will never meet no matter how long you extend the lines.
When you put two lines on the plane, one of two things will always happen.