After the mens 4x100 relay final races in Rio on August the 19th the commentators said they exchanged the baton outside the box.
What does that mean?
4x100m relay are composed by 4 runners that run approximately 100m each. To avoid that a faster athlete run a longer section are imposed limits for the passage of the baton.
In the image below you can see those takeover zones (red boxes) on a lap
Yesterday (August 18th 2016) Gatlin has touched his mate out of those takeover zone
The baton shall be passed within the takeover zone. The passing of the baton commences when it is first touched by the receiving athlete and is completed the moment it is in the hand of only the receiving athlete. In relation to the takeover zone, it is only the position of the baton which is decisive. Passing of the baton outside the takeover zone shall result in disqualification
To add to Ale's thorough answer: in the case of any disqualification in a major athletics event, the official results will usually cite a specific rule in the IAAF competition rules (which Ale linked). If you look up that rule you see what violation they're being disqualified for. In this case it wasn't immediately obvious which exchange was the problem from the results, but often the rule cited in the results gives you the clue you need to explain the disqualification.
They have a set margin of distance called the exchange zone to hand off the baton. The USA team handed the baton off before the exchange zone started therefore being disqualified.