Purple symbolizes nobility of purpose, spiritual leadership, spiritual teaching, regal power and authority in spiritual matters. It signifies you are a spiritual leader / teacher. Spiritual leadership works through empowering others to be able to face their own challenges and works through female energy.
Purple is the color of the crown chakra which is associated with spiritual understanding. Purple has long been associated with leadership, royalty and religious dress. In Roman times only leaders and boys under 17 years old (potential future leaders) were allowed wear the color purple.
Lilac indicates responsibility. For example, to dream of women exercising in lilac leotards tells you it is your responsibility (lilac) to develop your emotional expression (women exercising).
Indigo is the color of the brow chakra. This chakra is often depicted as the third eye and in dreams indicates you are psychic.
In a healing context purple brings spiritual peace, heals insomnia, tumors of the brain and calms highly-strung, excitable people.