Refraction is basically the bending of light. This occurs when light passes from one medium (substance) to another.

You've probably seen this effect if you've ever looked at a straw in a clear glass of water. It looks bent because the light is bending, but the straw is completely straight.

The big equation used to discuss refraction in physics is called Snell's Law and it states:

n1sinq1 = n2sinq2

where the n's are the indices of refraction of the two materials (for vacuum, n=1) and the angles (q) are the incident angle (the way it hits the surface) and the refracted angle (the way it leaves)