"Trade agreements are when two or more nations agree on the terms of trade between them. They determine the tariffs and duties that countries impose on imports and exports. All trade agreements affect international trade." 
There are three types of trade agreements. The first one is called unilateral trade agreement. That's when a single country appoints trade restrictions (in some uncommon cases countries loosen their trade restrictions) and no other country reacts to it.
The second type of trade agreements are the bilateral trade agreements. These are contracts between two countries (unions). Usually taxes and duties are lowered. Difficulties while negotiating usually focus on key protected or subsidized domestic industries. The largest bilateral agreement would be the Transatlantic Trade and Investment Partnership, better known as TTIP. This deal is currently in the negotiation phase but officially paused by the US government.
The third type is even more difficult to negotiate. Multilateral trade agreements involve three or more countries. The biggest of its kind is the North American Free Trade Agreement (short NAFTA). It is between the United States, Canada and Mexico.
The World Trade Organization (WTO) enforces the agreements once they are in place. The WTO also responds to complaints if the agreement is disregarded. At the same time the WTO tried to lower trade barriers among every member of the WTO by itself. The latest round (Doha Development Agenda) is considered failed after the disparities between some members were too big.
Another trade agreement to mention is TPP (Trans-Pacific Partnership). It was already fully negotiated (after 7 years) when the United States quit the agreement. It is not clear how TPP will look like in the future.
There are multiple advantages and disadvantages of trade agreements.
Probably the biggest advantage is the growth of economy. NAFTA for example increased the US GDP by 0.5%.
One disadvantage of trade agreements is that a lot of jobs are getting moved to cheaper manufacturing countries (job outsourcing).