Depends on your filing status, but you get taxed a certain percent on the amount that falls into that bracket.
For a single filer,
$0 to $8,700 is taxed at 10%, so a max of $870.
$8,701 to $35,350 is taxed at 15%, so a max of $3,997.50 (plus the $870 from the previous bracket, $$4,867.50)
$35,351 to $85,650 is taxed at 25%, so a max of $12,575 (plus the two previous brackets, $17,442.50)
etc...
That's why a pay raise will never decrease the amount of money you make due to paying more taxes. Once you hit the top of the tax bracket, you're not getting taxed anything additional on that bracket. The tax brackets are also on adjusted gross income minus deductions, not gross. Which means you can decrease your taxable income with deductions so you fall into a lower tax bracket.
So you making $95,000, can reduce your gross to somewhere in the 25% bracket.
Or, if you have an army of accountants (like Mitt Romney), you can reduce your millions of dollars in income so much that you're only paying 13% or whatever (that also includes the fact that capital gains, which are in the first section of income on the 1040, are taxed at 15%).