To dissociate is to break apart from someone, such as an employee leaving a business or a spouse leaving a marriage.
Dissociate is the opposite of associate. It comes from the Latin dissociare, which means basically "to disunite." To dissociate is to stop associating with someone. If a relationship ends, the two people dissociate from each other. If a person boycotts a business, she dissociates from it. Two business partners who have a fight and then split up have dissociated. When you see the word dissociate, think "break-up."