A cut in income tax will lead to a rise in income for consumers, as they are now paying less tax. This should lead to an increase in consumer spending, which boosts aggregate demand. An increase in aggregate demand will lead to an increase in the price level and an increase in real GDP, ceteris paribus (i.e. all other factors remaining the same). As consumers feel more confident due to higher disposable incomes, a positive multiplier effect is likely. However, lower tax rates will not affect the poorest in society who do not earn enough to pay tax, and depending on how the tax cut is formulated, may unfairly advantage those on very high incomes who may not increase spending in response to a rise in disposable income.
However, as tax levels are cut, this will reduce government revenue. Supposing that government spending remains the same, this will reduce the government fiscal surplus or increase the government fiscal deficit. This can have ongoing consequences if a fiscal deficit is maintained.