Disposable income is the part of GDP that’s eventually left to individuals after all taxes(personal taxes and business taxes) have been paid available for spending and saving. Subtracting company net saving (company saving less capital depreciation) and direct taxes from NI (national income) gets you the DI.
In plain words, disposable income for individuals is the part of total earnings deprived of all taxes paid and profit reserved for companies, which is the amount available for spending or saving.