The Big Four record labels are the four major records labels. They are:
Artists who are signed to a Big Four record label are either signed to the central label or signed to a subsidiary of the label. For instance, a band may be signed to Sony, or they may be signed to the Sony subsidiary label Columbia Records. These subsidiary labels have their staff and usually sign their own artists and make most of their own financial decisions. However, they are answerable to the "main" company, which sets their overall budget and makes decisions like reducing staff at the subsidiary.
In this respect, the hierarchacal structure of a major label can be quite complex and can differ a bit from label to label. In essence, a Big Four label is a corporation that manages several smaller businesses. In addition to the labels that are divisions of the major, these Big Four record companies also sometimes offer distribution to indie labels. Under these deals, the major label offers the indie's releases to stores along with their own releases, but they do not have a say in what albums the indie releases or how the indie manages their label.