A Common Market (CM) is a stage of economic integration.
In a CM, all factors of production (capital and labor) can move freely within the market.
For instance, imagine there are three nations: A, B, and C. A and B are in the common market, C is not. A has to allow all of its citizens to move to B, all of its investors to invest in B, open its border to B workers, and its capital markets to B investors (and vice versa). Economically, the common market helps outside nations, because of its greatly increased efficiencies, but it tilts the political balance of power.
Common Market is the first stage of economic integration where national character is lost. (If you don't believe this, imagine what would happen if the United States of America formed a Common Market with the United Mexican States.)
The European Community (EC) (the forerunner to the European Union) is arguably the most successful common market in history. However, states-rights activists (such as the Supreme Court and yours truly) maintain that the USA is common market, and not an economic union.