A Customs Union (CU) is a stage of economic integration.
In an CU, the trade policy of member states against non-member states is decided jointly. This eliminates the beggar-thy-neighbor effect of Free Trade Agreements, where the nation with the lowest external tarrif receives all imports from outsiders, which it then distributes to other members.
For instance, imagine there are three nations: A, B, and C. A and B are in the CU, C is outside it. If either A or B want to change its tarrif against C, it has to get the other member to go along with it. This can happen either by informal agreement (the nations all get around to it), formally (through a definite mechanism), or through an international body. In the real world, though, the largest member often gets to dictate terms.
An important part of foreign policy, trade policy, is all but lost in a CU. "Sanctions" must now be imposed multilaterally.
The most successful customs union of all time was the German Customs Union (GCU) (the precursor to the German Empire).