An incentive stock option gives you the right to buy company shares at a fixed strike price. What sets ISOs apart from other options is tax treatment. When you exercise, the difference between the strike price and the current value (the spread) is not taxed as ordinary income the way it is with other options.
The catch is the alternative minimum tax. The spread does count as income under AMT rules. Exercise 10,000 shares at a $2 strike when they are worth $20, and you have a $180,000 AMT adjustment even though you received no cash. For a private company where you cannot sell, that can mean a real tax bill on paper gains.
If you hold the shares at least two years from the grant date and one year from exercise, the whole gain from strike to sale price is long-term capital gain, taxed at lower rates. Sell sooner and the spread becomes ordinary income. Only the first $100,000 of options (by strike value) that become exercisable in a year can be ISOs; the rest are treated as NSOs.
The common mistake is exercising a large block late in the year without running the AMT numbers. Many people exercise in smaller pieces, or early in January, to see the full-year picture before committing.