What is the reason there are different coloured light sabers in star wars?

Answer 1

Each lightsaber contains a crystal, unique to the jedi/sith that wields it. To complete their jedi training, a jedi must find the crystal to complete the construction of their own lightsaber.

In the early days of the galaxy, the Sith had both purple and red lightsabers, while the jedi have yellow, blue, and green. Later on, the Sith abandoned (for the most part) purple lightsabers, and jedis that are on the light-side of the force, but can also wield dark-side powers for good purposes, wield a purple lightsaber. Mace Windu, for example, uses a purple lightsaber because he can also use the dark side; his lightsaber form requires him to use it.