AMT was invented by the IRS and Congress in reaction to rich people who came up with clever ways to avoid paying their fair share. See Warren Buffett's recent diatribes on this subject for more gory details on the effects of aging on one's brain. AMT evolved into an onerous burdensome tax structure that is now being reconsidered in Congress.
Specifically, AMT adds back items into the "adjusted gross income" line that everyone fills out on their forms for the IRS. Some things that used to be deductible aren't deductible any more like charitable contributions over a certain percentage of your income, etc.
For The Seven, all you really need to know about AMT is that it's neither "minimum" nor "alternative."