If your total income for the year is in the lowest income or tax bracket, you pay no tax. Once you move out of the lowest bracket and into the next one, you have crossed the threshold from paying no tax to paying at least the lowest rate of tax.
If you are an Australian resident for tax purposes, the first $18,200 of your yearly income is not taxed. This is called the tax-free threshold. Therefore, by claiming the threshold, you reduce the amount of tax that is withheld from your pay during the year.