A chancellor is a leader of a university or a college. This title is mainly used in the Commonwealth nations. In other countries, such as the United States, it is more common to call him/her the university president.
The chancellor is often just a ceremonial figure. This means he or she does not make many decisions inside the University. He/She is just a person who is chosen to represent the University at official events and with other organizations. In this case, the Chancellor might not even live close to the University or take part in meetings there. For example, at the University of Cambridge the chancellor is a person who has done something important in his life, and is in some way connected to the University. Prince Philip, Duke of Edinburgh was the Chancellor at Cambridge for 36 years.
The vice-chancellor of a university is instead the chief executive. He/She is the one that makes all the decisions, goes at regular meetings and has the day-to-day duties to do. The vice-chancellor is often very closely linked to the University: for example, he/she might be a fellow there, who decides to take on additional responsibilities. The vice-chancellor might also represent the university at important events if the chancellor is not available.