Tax bracket

Tax brackets are the divisions at which change in a  system (or an explicitly  system, although this is much rarer). Essentially, they are the cutoff values for taxable income—income past a certain point will be taxed at a higher rate.

Example
Imagine that there are three tax brackets: 10%, 20%, and 30%. The 10% rate applies to income from $1 to $10,000; the 20% rate applies to income from $10,001 to $20,000; and the 30% rate applies to all income above $20,000.

Under this system, someone earning $10,000 would be taxed at a rate of 10%, paying a total of $1,000. Someone earning $5,000 would pay $500, and so on.

Meanwhile, someone earning $25,000 would face a more complicated calculation. The rate on the first $10,000 would be 10%; the rate from $10,001 to $20,000 would be 20%; and the rate above that would be 30%. Thus, they would pay $1,000 for the first $10,000 of income (10%); $2,000 for the second $10,000 of income (20%); and $1,500 for the last $5,000 of income (30%); in total, they would pay $4,500, or an 18%.

In practice the computation is simplified by using or  of the linear equation for the tax on a specific bracket, either as tax on the bottom amount of the bracket plus the tax on the marginal amount within the bracket:
 * $$\$3\,000 + (\$25\,000 - \$20\,000) \times 30\% = \$3\,000 + \$1\,500 = \$4\,500,$$

or the tax on the entire amount (at the marginal rate), minus the amount that this overstates tax on the bottom end of the bracket.
 * $$\$25\,000 \times 30\% - \$3\,000 = \$7\,500 - \$3\,000 = \$4\,500.$$

See for details.