Basically they will lodge your "income" as the bare minimum so that there are still some salary expenses on their books, however through close scrutiny of the employment laws, you will not be offered any of the usual benefits.
Example:
On the books you get $400 a month; but off the books you get $2K cash in hand. The employer then has no obligation to pay superannuation as it is under the $450 threshold per month before it's applicable, nor will there be any PAYG payable as your reportable income is so low. Payroll tax is a non-issue, as a company who engages in this will probably not be anywhere near the $600K or so required.
What this means for you...
* If you get injured at work, you will not be covered and you'll have to take the employer to court
* If you want to get a loan, you won't have much luck as you won't have any official "income" to show
* If you start getting fancy with your financials, chances are you'll get audited by the ATO
Even though all things point to the employer breaking the law, it works both ways. Say you engaged in such employment for many years and finally something came unstuck. Chances are, you'll be liable for tax evasion as you did not report that income when filing your returns. Saying you have a dodgey employer is not an excuse.
Back onto the employer side, the "contractor" excuse is not valid for the fact everything you do points to you being an employee. The laws have tightened around this and simple tests surrounding principle sources of income, time spent on 'contract', etc will quickly make you an employee, not a contractor.
As Duncan said, the only real upside to being paid cash is the fact you will have a job... for the likes of working travelers, minors - they may simply not care about the protections offered otherwise.