People and organizations who push for "fair trade" are advocating for trading practices that will not "unfairly" exploit the resources or labor of developing countries.  They want to end the somewhat colonial nature of trade with developing countries and replace it with a model that allows the developing countries (and the individual workers there) to move more towards economic self-sufficiency.

Fair trade is typically applied to commodities such as coffee.  Such commodities are things that are historically produced at the lowest cost possible, which often leads to practices that harm the environment and/or which create poor working conditions and low pay for the workers.  The fair trade movement tries to create demand for coffee (in this case) that is grown in more sustainable ways and with better pay and working conditions for the workers.

The overall concept, then, is one in which the "bottom line" of profit is seen as less important and consumers are encouraged to buy based on how the product impacts the environment and the workers in the country where it is produced.