First a note on usage: in the UK and Australia you will hear the term postgraduate. In the US people drop the first part and simply say graduate. Both terms refer to the second level of study at the university.
An undergraduate degree (S1) is a prerequisite or requirement for study at the graduate level (S2). A masters degree is perhaps the most common name for a graduate level degree. The options for graduate study vary considerably depending on the field of study. Here are a few examples:
- A masters degree in engineering (MS in Engineering) may be completed in 1 — 2 years
- A masters degree in business is known as an MBA and usually takes 1 year to complete
- A Juris Doctorate is required to practice law and requires 3 years to complete
For students who plan to continue on to a PhD (S3) or similar degree, the masters level may be just a stepping stone.