CSP - Commonwealth-supported place: student contributes toward cost of course.
DFEE - Domestic fee-paying: student pays a tuition fee (full cost of the course).
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CSP is basically the new system of HECS. The government pays part of your education and you also don't have to pay it right away, it gets garnished from your salary when you start earning a certain income. It depends on what course you take, but typically per year CSP costs around $4000-6000. This is what most students use.
DFEE is the new equilalent of full-fee paying, which means you get no contribution from the government; you have to pay the entire cost of your course. You also have to pay each semester's fee upfront, it is not a debt like CSP where you pay it back later. It depends on what course you take, but typically DFEE costs around $16,000-$19,000 per year. The advantage of DFEE is that DFEE places take students with UAIs up to 5 points below the normal cut-off (though it can be less).
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More information is available from
Going to Uni (Australian Government).