A cut in income tax rates would be one part of a classic Keynesian fiscal policy approach to combatting a recession.
Keynesians emphasize the importance of aggregate demand in macroeconomics. That means that, to them, an income tax cut is important because it will increase aggregate demand.
It will do this by increasing consumption. A tax cut will give people a higher disposable income. By definition, looking at the equation for the consumption function, an increase in disposable income makes for an increase in consumption.
This is because C = a + c Yd where
a is autonomous spending, c is mpc and Yd is discretionary income.
If Yd goes up and everything else is constant, C (consumption) must go up as well.