Tax cuts are a reduction in taxes. How they affect the economy depends on the type of tax being cuts.
Income tax cuts are cuts in income taxes to individuals and families. They can be a reduction in the income tax rate, like the Bush tax cut of 2001, also known as EGTRRA. They can be a one-time reduction, as with the Bush tax rebate of 2008. These both were mailed to tax payers in the form of rebate checks.
The Obama income tax cuts were a fixed reduction, like the 2008 Bush tax cuts, but taxpayers received them through a decrease in tax withholding instead of a check. Many people didn't even realize they had gotten a tax cut.
Individuals can get tax cuts for specific purposes. For example, the Economic Stimulus Package gave an income tax cut equal to the sales tax on new car purchases. It also provided $17 billion in tax cuts for households who invested in renewable energy sources.
Businesses tax cuts reduce taxes on profit. The Obama tax cut gave a variety of incentives to small businesses. Business are also helped when investors get tax cuts because it's like an incentive to buy business stocks. For example, the Bush tax cuts of 2003, or JGTRRA, reduced the maximum tax rate on long-term capital gains and dividends to 15%.
How Tax Cuts Work
Tax cuts boost the economy by putting more money into circulation. They also increase the deficit if they aren't offset by spending cuts. As a result, tax cuts improve the economy in the short-term, but depress the economy in the long-term if they lead to increased federal debt.
Once tax cuts are put in place, they are difficult to revoke. Why? A tax cut reversal feels like, and has the same impact, as a tax increase. That's what happened when the Bush tax cuts were due to expire in 2010.