Disposable income is total personal income minus current taxes on income. In national accounting, personal income minus personal current taxes equals disposable personal income or household disposable income. Subtracting personal outlays (which includes the major category of personal [or private] consumption expenditure) yields personal (or, private) savings, hence the income left after paying away all the taxes is referred to as disposable income.
Restated, consumption expenditure plus savings equals disposable income after accounting for transfers such as payments to children in school or elderly parents' living and care arrangements.