Why do I need a tax number?
Getting a tax file number will make sure that you are taxed at the appropriate rate whilst in Australia. As a traveller you will be taxed as a non-resident at a rather high 30%. Its easy to apply for one just have your passport to hand and a physical address in Australia that they can send the details to.
Can I claim my tax back?
If you stay in one place for more than six months then you may be able to claim that your behaviour is that of a resident and so you can claim a tax refund on the higher non-resident rate you have been paying. There a number of organisations in Australia that will help you with this just ask in your local hostel or job agency.