Fair trade is the market-based answer to charity. Instead of perpetuating the charity cycle, which just creates dependency on handouts, fair trade principles ensure that farmers get a fair price for their harvest, based on the market, i.e. supply and demand. Trading is done directly, without a middleman, which would otherwise take a chunk out of the farmer's price. These transactions generally involve agricultural products which are sold for export.
The most commonly Fair Trade certified products are coffee, cocoa, sugar, tea, bananas, honey, cotton, other produce, and flowers.
So what does this have to do with fashion? The most popular fiber used in apparel, cotton, is an agricultural product, and has been eligible for certification for many years.
In addition to fair payment, fair trade ensures that working conditions are safe, farm workers get a living wage, and workers maintain the right to organize for collective bargaining.
All of these principles create positive impacts, like allowing working families to eat better quality food, keep their kids in school, receive healthcare, improve their housing, and save and invest for the future.
And the environment benefits, too. Fair trade agreements require that local ecosystems are protected, and farmers are encouraged and supported in transitioning to organic agriculture
Each fair trade certification organization has its own variation on these principles, so be sure to investigate what they're actually certifying, if you want to know more about a particular issue. Fairtrade International is basically the global leader on Fair Trade standards. Fair Trade USA certifies some products being imported to the US, and recently started certifying apparel.
All that being said, many companies use the phrase "fair trade" to describe their production or sourcing model, which may or may not be certified by a third party. It's always a good idea to do a little investigating, or even send them an email, to directly ask what they mean by that, what standards they follow, how do they audit, etc.