A lens refracts light by slowing it down and bending it with regard to the "normal" line, a line at a right angle to the surface of the lens. When the light passes through the far side of the lens and speeds up, it bends away from "normal," refracting further.
When the focal point is behind a lens, as when a person is looking at an object, the light moves toward that person's eyeglasses or contact lenses in parallel lines. When the light rays hit the lens, they are no longer traveling through the air; instead, they are traveling through a solid, generally glass or plastic. The increased density of this new substance slows the light down; even though the change of speed is infinitesimal, it is enough to alter the path of the ray of light.
The new path for the light ray adjusts to the "normal" line -- a line perpendicular to the surface of the lens. The light ray does not turn to follow the line but instead takes an angle between its original one and that perpendicular line. On the other side of the lens, moving out of the lens causes another change in speed, because the density of its environment has lessened once again. The light ray takes another turn, heading to meet other formerly parallel light rays at the focal point.