One of the best reasons for postgraduate study is money. While research methods or results vary, studies consistently show people with postgraduate qualifications wind up in better paid jobs, sometimes earning as much as 30% more than people with just a bachelor’s degree. There's a school of thought that this is the result of "degree inflation": with a higher proportion of the population going through university, a bachelor degree isn't as valuable as it once was.
Postgraduate study allows you a great opportunity to specialize in a subject. While going to university means switching from or three or six A level subjects to one or two degree subjects, postgraduate degree courses let you concentrate on a specific element of one subject. If you have a particular interest in a topic, or if you enjoyed some aspects of your bachelor course more than others, postgraduate study could be a great way to focus.
Contrastingly, postgraduate study can allow you to broaden your horizons. It may be that your chosen degree turned out not to be your preferred subject, or you may simply have had other academic interests that you didn't pursue as an undergraduate. To some extent postgraduate study can allow you to quite literally change course, though you may be limited by entry requirements.
Another important aspect of postgraduate study is that it can either be very useful or an actual requirement to enter certain professions. For example, people wanting to become a barrister or a teacher will usually need a specific postgraduate degree. With some jobs, the key may be enhanced emphasis on vocation training. For example, many prospective journalists take a more general bachelor degree subject to broaden knowledge or get experience of research or analysis skills, before going on to a specific postgraduate journalism course to learn how to translate this knowledge into practical reporting skills.
It's important to remember that some reasons for postgraduate study aren't so compelling. At one time it was a way to simply put off the "real world" or extend the student lifestyle: today tight finances or increase competition mean that isn't the case, or anyway a postgraduate course has a much higher work-play ratio. Simply doing a postgraduate course because you aren't having any luck finding a job isn't a solution: it's only buying you an extra year in many cases, or will bring added financial pressure. or you may need to think twice if you are doing an extra course just to keep parents or tutors happy: postgraduate study has to be your decision.