Not a drug courier, silly. In airline lingo, a courier is someone who travels without luggage to fill a seat a company has purchased in order to send goods or papers. So you simply take a seat that otherwise would be physically empty. Companies resell them at massively discounted prices because they need a warm body to accompany their stuff and make sure it gets where it needs to go. It can also be cheaper for a company to sell the seat at a major discount than to send the stuff over via airmail.

The benefits to the company are 1) the swift transportation of important items and 2) faster customs clearance than regular cargo. The benefit to you is a cheap ticket, anywhere from 50% off or more. The drawback of being a courier is the possible lack of advance notice about your flight and traveling with only a carry-on bag, especially for longer trips. But it's crazy cheap, especially for international flights. Note that most courier travel companies require you to become their member for an annual fee.

Some places to contact include:

You should now be satisfied that your relentless search has yielded the lowest fare possible. So book the trip and board the plane. Now you can be the obnoxious seatmate, boasting about your unbelievably cheap fare. Isn't irony great? Sit back, enjoy the ride, and don't forget to pass the peanuts.