There are many economic factors that can be affected when taxes are raised or lowered, depending, for example, on what taxes are involved.
Raising some taxes can lower the supply of various goods. For example, if a gasoline tax is increased, the supply of all goods that have gasoline as an input will decrease. This is because the price of producing those goods will increase, which is a cause of a decrease in demand.
As another example, an increase in sales taxes could reduce the marginal propensity to consume. If people have to pay more in tax every time they buy something, they may well decide to buy fewer things. If they do, the marginal propensity to consume declines and savings should increase.