Federal income tax is generally the "bulk" of your tax, implemented in marginal (read: tiered) amounts as you earn more and more money. Everyone in the country is affected by this, and the money goes to the federal government, which is generally responsible for "country-wide" programs, policies, and the armed forces.
Each state has its own income tax (and some have no income tax at all, like Florida and Alaska!), and that applies only to residents of that state. It's generally less than federal income taxes and pays for state-specific stuff. Some states are high, some states are low.
You may also have local taxes as well, specific to your city or town.
All of these add up to form your total tax bill for the year.