Before Mace Windu’s purple lightsaber showed up, watchers of the original Star Wars trilogy were treated to blue, green, and red sabers.
Blue was the color of Jedi Knights with more aggressive fighting styles. Green was for teachers and mystics with a close affinity to the Force. Red was the color of grief, anger, and hate, therefore belonging to the Sith.
More obviously, purple is a sign of rarity. Since it is used much less than its counterparts, it is a special color for a special combatant. So the blazing purple blade symbolizes the rarity of wise, compassionate, and powerful fighters like Mace Windu.
But it is more than that. To understand the purple lightsaber more, it is important to understand Vaapad.
There are seven known fighting styles in the Star Wars universe. The 7th, known as Juyo, is the most aggressive among the others. Since it harnesses aspects of the Dark Side, it is usually forbidden to Jedi Knights.
Mace Windu used form 7 to develop a similar fighting style known as Vaapad. Vaapad is best described as using the Dark Side to one’s own advantage while battling a member of the Sith.
When a Jedi uses Vaapad, he absorbs the darkness of his Dark Side opponent. He then channels this darkness and throws it back at this opponent. Since it means delving into the Dark Side, it is a dangerous method that can be used only by those who have a strong affinity with the Force.
Mace Windu is a unique Force-user. Although he allies himself with the compassion, sympathy, and selflessness of the Jedi, his use of Vaapad gives him access to the power of the Dark Side.
This is the clearest answer to the question of why Mace has a purple lightsaber. Since purple is a mixture of blue and red, a purple lightsaber wielder harnesses both the power of the Light and of the Darkness within him.