Taxable income is the income against which tax rates are applied to compute the tax paid.
For a business, it is gross income less allowable expenses and other deductions. For individuals, it is "adjusted" gross income less the standard exemption and allowable deductions (either standard or itemized if exceeding the standard)
In the United States, the general rule is that all income is subject to tax, unless a specific exemption is granted (such as municipal bonds). Concurrently, deductions are limited to those specifically allowed by law (such as charitable donations or property tax over the standard deduction).