Government co-contributions is the Government providing matching contributions to your super if you earn less than $51,021 per year (before tax) and make after-tax super contributions. If you earn less than $36,021 then the maximum co-contribution is $500, based on 50c from the Government for every $1 you contribute. The co-contributions will reduce the more you earn until you reach the limit of $51,021 at which time you are no longer eligible to receive the co-contribution.
To receive the co-contribution you will need to lodge a tax return for the financial year. The Government will then work out how much you are entitled to. Assuming you are eligible, the Government will pay the co-contribution directly into your superannuation fund.