Taxable income is all of the income that a person makes in a year minus the deductions that are allowed by the government. It is the money that the government can draw taxes from. This amount varies widely from person to person. The government has the legal authority to take taxes from the taxable income of its citizens.
There are many deductions in the U.S. tax code that can reduce a person's total taxable income. For example, deductions may be given for donations made, home mortgage interest paid, medical expenses paid, and a number of other things.
Paying taxes that are owed is not optional; citizens have a legal obligation to pay the taxes that they owe to the government. If they don't, then they can face an audit from the Internal Revenue Service. This could be followed by legal consequences, even including jail time in some cases.