Shade of purple is important in dream interpretation.

Mauve represents endurance, while Lilac represents responsibility.

Violets and purples are rich colors and often convey wealth, extravagance, and preciousness. 

Purple was first associated with royalty because of its rarity and expense.  That's how the color became a symbol of wealth and power. 

The Purple Heart is awarded to members of the U.S. Armed Forces who have been killed or wounded in action against an enemy. It may also be awarded for maltreatment endured while a prisoner of war. Why is the medal given to our wounded service people called a "Purple Heart?"  My best guess is that it symbolizes the power of the wounded person to survive.

Amethyst, variety of quartz, differing from common quartz and rock crystal chiefly because of its violet to purple color, which is caused by the presence of compounds of iron or manganese. It is a birthstone for February and is used to make seals and rings. The finest specimens occur in India, Sri Lanka, and Brazil. Amethyst is common in Europe and in many parts of Scotland.

In heraldry, purple depicts royalty.

Other connections include knowledge, old age, magic, and enchantment.