The Alternate Minimum Tax was created to prevent those with sufficiently high incomes from finding sufficient loopholes to avoid paying any tax at all. If your taxable income is above a certain level, a minimum tax is specified, and you must pay at least that amount regardless of what tax you calculate by applying all the exemptions and deductions you can find.

The "trigger amount" at which the AMT becomes applicable has been changed many times, and hardly anyone knows for sure what it is; but the "cliff" results in expiration of "temporary limits" so that people in approximately the range between $75,000 to somewhere in the vicinity of $125,000 (?) who generally didn't pay according to the AMT will be subject to it if no other changes are made by the current session of Congress. The AMT calculation generally disallows certain "deductions" that would otherwise apply, resulting in a significant increase in the tax. The tax rate is essentially the same as for income calculated otherwise, but with certain deductions disallowed.

The AMT apparently does not apply to the Capital Gains Tax which applies a rate of 15% rather than the 26%(?) rate for earned income.

For a complete explanation one can look at the Wikipedia Explanation which I'm sure will make it all exceedingly clear**.

** (Like Hell it will.)

John