It's a ministerial position. He is a senior member of cabinet. The role of ministers are never really officially outlined - they are more assumed.
He has no actual power, he is merely the "financial spokesman" for the government. He drafts fiscal policy, these drafts are powerless without the backing of Parliament. In the case of the current government our Treasurer is next in line for the throne - he is well liked and endorsed by Howard. So basically anything Peter Costello says, it can be assumed that Howard is in full support of it. Members of Parliament in Australia almost always vote with their party, so it can be assumed that anything Costello proposes will be enforced by the full power of the federal legislature (well the majority of it anyway!).
This may put the Treasurers proposals through the House of Representatives (lower house), however the Senate (upper house) generally requires some dealing. For example, an independent Senator will vote for the legislation if something is ammended. This of course will not be a problem in the near future for the Liberal-National Government when they assume control of the Senate.
Hope this helps!