Alternative minimum tax (AMT) is a supplemental income tax. It won't be relevant for most taxpayers, but those with high incomes and in other special situations may have to deal with it. One particular situation when the AMT may be relevant is when startup employees exercise ISOs.
Stock Options: ISOs vs. NSOs
What may seem like a bland choice (whether to grant ISOs or NSOs) can have massive tax implications down the road for startup employees and contractors.