The refractive index is a measure, indirectly, of how much the speed of light changes as it moves from one medium or material to another. The denser the medium the more the speed of light slows down. This effect is seen, for example, if you look at an object laying on the bottom of a swimming pool. The object's actual position is different than where it seems to be when looking at it from above.
When light hits the surface of a piece of glass at an angle its speed changes as it goes from the air (low density) to the glass (much higher density) and the light rays bend. You can see this bending because a rainbow of colors is produced.