What is a free-trade agreement?

A free-trade agreement is an agreement between two or more states in which the signatories agree to trade with each other without any restrictions. So if country A wanted to sell cars to country B, and country B wanted to sell wheat to country A, then under a free trade agreement they'd be able to do so without incurring any taxes or tariffs.
Though most states in the modern world claim to support free trade in principle, in practice they regularly impose tariffs on selected imported goods, usually as a way of protecting domestic industry from foreign competition. Tariffs have the effect of increasing the cost at which exporting countries can bring their goods to a foreign market, with the knock-on effect of price increases for consumers. This is just one of many reasons why free-trade is regarded as generally beneficial, because it tends to reduce costs for both businesses and consumers alike.
In practice, however, the benefits of free-trade agreements are not always evenly distributed. For example, it is argued by some critics of NAFTA, a free-trade agreement concluded between the United States, Canada, and Mexico in 1994, that the generation of millions of new jobs under the agreement was offset by the loss of large swathes of American manufacturing. One of the many negative consequences of such large-scale job losses was the weakening of labor unions, thus undermining pay and conditions for American workers in general, not just those in manufacturing.