The Part-Year Tax-Free Threshold Adjustment applies only to those people who either became or stopped being an Australian resident for tax purposes during the financial year.
Australian residents all receive a tax-free threshold - a certain amount of income that is exempt from tax. For the 2011-2012 financial year the tax-free threshold is $6,000 but for 2012-2013 onward it will increase to $18,200.
Those whose residency status changed part way through the financial year still get a tax-free threshold, but only a portion of what the normal residents get. The tax-free threshold for these part-year residents is pro-rated based on the number of months they were a resident. For example, if you were a resident for only six months of the 2011-2012 financial year, your tax-free threshold will be $3,000.
If you were a part-year resident, you need to declare on your tax return the date your residency status changed and the number of months out of the financial year - including the month that you either became or stopped being a resident. The ATO will then use this information to calculate your individual tax-free threshold.