There are a fair few threads on this (just search UMAT and there are about 6 pages of threads). Basically it is an aptitude test comprising of three sections.
The first section is logical reasoning and problem solving, which in short is a whole lot or reading, analysing diagrams and answering questions on them.
The second section is understanding people, where you are given dialogues on different situations and you are asked different questions about the emotions the people may have been feeling (bit of a vocab test if you ask me).
The third section is non verbal reasoning where there are patterns and shapes and you are asked to put them in order and choose the middle one, choose a shape which fits best into the picture etc. It is mainly finding patterns.
This is just a short description. I suggest you get your hands on the Acer books, as they will give you a better idea of the structure (
http://umatweb.acer.edu.au/index.php?option=com_content&task=view&id=21&Itemid=3)
You are given you results a few months later and you are given a score. Basically your score needs to be high enough to get you an interview. You would want to be aiming for about the 90th+ percentile. There is also a fair bit of information on the website "medstudentsonline" (
http://www.medstudentsonline.com.au/).