Short for Bell Operating Company, which also known colloquially as a Baby Bell.
This is the local or regional telephone company which owns and operates the telephone lines that run to customers' homes and businesses, and to Class 5 Switches. They have connections to other COs, Tandem offices, and may connect directly to IECs (the big players in the telecom game) like MCI WorldCom, AT&T, or Sprint.
These are the companies that were formed after the AT&T Divestiture of the 1980s. The 1982 Modified Final Judgement in that case originally defined the role that BOCs would play in the U.S. telephone system, although that role has grown and changed somewhat since then. Each BOC may service more than one LATA, but they are generally constrained from providing long distance service between LATAs.
In 1974, the United States Department of Justice filed an anti-trust suit against AT&T charging anticompetitive behaviour. The DOJ sought breakup of the AT&T-owned Bell System. The suit went to trial, and in 1982, AT&T agreed to divest itself of all its Bell System holdings, 22 BOCs in all. In 1984, the divestiture was completed, and the 22 BOCs were no longer a part of AT&T, but held by seven regional holding companies, also known as RBOCs, for "Regional Bell Operating Companies."
Also short for Blue Oyster Cult, but that's another matter entirely.
Sources:
http://www.navyrelics.com/tribute/bellsys/index.htm - A Memorial to the Bell System: David Massey
http://www.ph4less.com/Glossary.html - Telephone Terminology Glossary