Postgraduate study is any study after your basic degree, be that science, engineering, arts, etc. There are two main options:
A Masters is usually one year long, and it qualifies you as someone with an "in-depth" knowledge of a particular field. To get a Masters, you're required to show that you have a detailed knowledge of that particular field. There are two types of Masters, 'Taught' and 'Research':
A Doctorate usually takes a minimum of 3 years, and typically around 4 years full-time, and it qualifies you to be a professional researcher. To get a doctorate, you need to make "an original contribution to knowledge". That is, they're not content with you knowing a lot of stuff, you have to show something that no-one in your field, anywhere, has shown before. You could typically do this by applying a new method to an old area, an old method to a new area, or a new method to a new area! Or something like that. The Doctorate also should prepare you for life as an academic: writing reports, scientific papers, meeting deadlines, interacting with other researchers at conferences, etc.
The academic life can be a dream or a horror, depending on who you talk to. Due to the lack of a structured work day, typically academics can come in (and leave) at whatever time they want, or take coffee breaks whenever they want. On the other hand, there are deadlines to meet in the form of theses, reports, papers, grant submissions. You could be working with the hottest equipment, or the shittest equipment. Academics can be harsh critics, and you will almost certainly have to defend your work on a regular basis through argument. You will be mostly expected to be able to work on your own (people are generally busy with their own things, and people helping people isn't always something that happens as fluidly as it should). Money isn't super at all (unless you've got a great grant, you work in a loaded Research institute, or you're a Professor), but it can all depend on the research lab you are in! On the plus side, it can of course be exhilarating to witness a result that nobody has before, or to feel you are on the edge of scientific knowledge - but there is a tradeoff you have to consider; academic life is not necessarily for everyone!