See here:
The council assesses the extent to which the Government's fiscal-policy objectives are being achieved. These objectives include long-run sustainability, the budget surplus target, the ceiling on central government expenditure and that fiscal policy is consistent with the cyclical situation of the economy. The council also evaluates whether the development of the economy is in line with healthy long-run growth and sustainable high employment. Additional tasks are to examine the clarity of the Government's budget proposals and to review its economic forecasts and the economic models used to generate them. Finally, the Council should try to stimulate public debate on economic policy.The site also says they do this with an 8 member council, assisted by a secretariat with only 2 employees. That's pretty thin for such an ambitious agenda. But from what I can tell they are doing a great job with what they have.
The Swedes started their Council about the same time as the PBO started up. It's like they're twins! As the Economist said, independent budget offices are a great way to build fiscal credibility for a country's government.
