Commonwealth Supported Places (CSP) is a government offering to subsidise higher education fees, usually by 2 thirds (~60%+), and it's available in all undergraduate degrees and some postgraduate ones. It's the BEST option if you have the student contribution amount (30%+) at your displosal (savings put aside), because you will have to pay it upfront for each subject your enroll in. Most students though don't have that upfront payment amount and they end up borrowing money to pay the full fee and have this debt dragged throughout their lives.
A simple example shows the difference:
Hussein wants to study a 2 years master of IT at University of Melbourne, he is a PR student. His options are one of the following:
Option A: Full fee payment
Total course fees: $64,944
Government payment: $0
Your payment: $64,944
What you payback to government (If you take a loan; i.e. HECS): $64,944 plus interest rate (named differently though).
Option B: CSP
Total course fees: $18,100
Government payment: $46,844
Your payment: $18,100
What you pay back to government: $0
Previously PRs were eligible to CSP offers but that changed with the changes introduced by the government a few weeks ago. The changes apply to new applications starting from January 2018, PRs will not be eligible to CSP but they will have the options to apply for HECS (government loan) to pay the full fees amount as explained above, and pay back the government when they are employed. However, if you are a PR and you are accepted in any university on CSP basis until end of this year, you will be a CSP for the remaining of your course (Master, Bachelor...etc).
Australian citizens will continue to have the CSP option, but with the continuous curbing of government's funding for higher education it's not certain that the option will be there forever.
Lastly, CSPs are offered by universities based on academic merit; they evaluate your application among other CSP applications, and rank students based on their academic merits. They issue CSP offers until their quota runs out. CSP offering is entirely at the university's discretion but it's certainly not impossible or exteremly difficult to get it, simply apply and wish for the best.