Tax brackets are part of a progressive income tax in order to apply a greater tax percentage to people who make more money. In the US, the tax rate you pay changes depending on what portion of your income is in question. So you may pay 10% on the first $20,000 of income and 15% on the next $20,000 of income.
The idea of tax brackets is that lower income earners spend more of their money on necessities and because of this they should pay a lower percentage of their income to the government. The problem with this approach is that lower income earners have a false sense of how much governmental services actually cost since the burden is greater on those with higher income levels. As a result they may be in favor of programs that they would be opposed to if everyone shared the same percentage of the cost.