Tax bracket
From Academic Kids

Tax brackets are the divisions at which tax rates change in a progressive tax system (or an explicitly regressive tax 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.
In a flat tax system, everyone is in the same tax bracket, and all of their income is taxed at the same rate, no matter how high their income may be.
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Example
Imagine that there are three tax brackets: 10%, 20%, and 30%. The 10% rate applies to income under $10,000; the 20% rate applies to income from $10,001 to $20,000; and the 30% rate applies to all income above $20,001.
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 $35,000 would face a more complicated equation. 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; $2,000 for the second $10,000 of income; and $4,500 for the last $15,000 of income; in total, they would pay $7,500, or about 21.4%.
Tax bracket myths
Contrary to popular belief, there is no situation in which a person ought to try to earn slightly less money — or create tax deductions by giving money away to charities — in order to "fall into a lower tax bracket" and lower one's tax burden across all of one's income. Reusing the example above, the myth is that a taxpayer earning $20,100 is in the 30% tax bracket, so if he could give away at least $100, he would drop down into the 20% bracket and pay onethird less tax in total.
The fact is that the above taxpayer is paying 30% tax on only $100 of his income ($30 tax). He's paying 10% on the first $10,000 of his income, and 20% on the next $10,000 of his income; the fact that he reached the 30% bracket doesn't change the tax he pays on the "bottom" $20,000 of his income. Put another way, a taxpayer in the 30% bracket earning $20,100 owes $3,030 in tax; whereas a taxpayer in the 20% bracket earning $20,000 owes $3,000 in tax. A person who wants to maximize his yearly income while factoring in taxation should simply try to earn as much money as possible; there is no "ceiling" above which it isn't profitable to earn money.
The kernel of truth within the myth is that people earning more money get more financial benefit out of creating tax deductions — such as giving money away to charities — compared to poorer people. To continue with the above example, Taxpayer A, who earns $15,000 and gives $1,000 to charity, effectively saves $200 in taxes; but Taxpayer B, who earns $50,000 and gives $1,000 to charity, effectively saves $300 in taxes. From time to time, a critic will complain that tax deductions benefit the rich more than the poor, which is true; but this is only true because the rich are paying a greater share of their income as tax to begin with.
Tax brackets in the USA
In 2004, the tax brackets for a single (unmarried) person were:
 10%: from $0 to $7,150
 15%: from $7,151 to $29,050
 25%: from $29,051 to $70,350
 28%: from $70,351 to $146,750
 33%: from $146,751 to $319,100
 35%: $319,101 and above
For example, a single (unmarried) taxpayer in the USA who earned $100,000 would owe $22,627 in taxes, for an effective tax rate of 22.6%.
Tax brackets in the UK
In the 20052006 tax year, the tax brackets were:
 10%: from £0 to £2,090
 22%: from £2,090 to £32,400
 40%: from £32,400 and above
This information was from http://www.hmrc.gov.uk/rates/it.htm