A beam of sunlight falling on a prism refracts and forms seven colored bands. What does this illustrate?

When the white light passes through a prism, it refracts into 7 bands of different colors. This shows that white light is composed of seven different colors. These seven colors are referred to as VIBGYOR, to represent violet (or V), indigo (or I), blue (or B), green (or G), yellow (or Y), orange (or O) and red (or R).  

Refraction is bending of a light ray as it goes from one medium to another. Speed of light is different in different media and hence it either refracts towards the normal or away from it. When that happens to white light, passing through a prism, its seven constituent colors move through the prism at different speeds and hence the white light gets split in seven different color bands.  

A similar splitting of white light into different colors is observed when it passes through water vapors in the atmosphere and we see a rainbow.

Hope this helps.