It’s a very complicated subject, but in a nutshell it’s effectively a minimum tax that hits certain higher and middle income tax payers.
Basically these taxpayers (and you may be one of them) have to calculate their income tax two ways to satisfy the IRS. If the alternative (AMT) calculation is lower than the regular calculation, you’re in the clear. If it’s more, you’re stuck with the higher tax.
Originally, the idea was to make certain that high income tax payers paid their fair share of taxes. Unfortunately, over time it’s begun to hit a much larger group of people than was originally intended.
Definitely consult your tax professional about this if you think it might affect you as you may need to increase your tax withholding to accommodate it.
If you do your own taxes, the IRS has an AMT calculator on its website to help you figure out your tax liability yourself. If you are using tax preparation software, it should be able to handle the calculation for you.