A commanding officer (or CO) is a term used to describe one's rank in relation to others within the same environment.
Military units
One meaning of commanding officer is the highest ranking officer and commander of a unit. On starships, the CO has the rank of captain or commander. On starbases, the CO is sometimes referred to as "portmaster" and was usually a flag officer. (TOS: "Court Martial", "The Menagerie", "The Deadly Years"). Some bases, however, are commanded by captains or commanders (Star Trek: Deep Space Nine, TNG: "11001001").
It is also possible for lower ranks to be the commanding officer aboard a starship for certain missions, such as the case with Lieutenant Commander Piersall aboard the USS Prometheus. (DS9: "Second Sight"). Another example can be found in 2368. At the height of the Klingon Civil War, Starfleet Command temporarily assigned a number of officers to command vessels that blockaded Romulan support of the Duras. (TNG: "Redemption, Part II")
On starships, it is general practice to address the commanding officer as "Captain," regardless of their actual rank or position. (DS9: "Behind the Lines")
In general, commanding officers are dressed in the colors of the command division, but there are some exceptions in Starfleet uniform usage.
In rare occassions, the commanding officer need not be a ranking officer, especially in dire circumstances. (DS9: "Valiant")
Dukat once claimed it was Cardassian tradition for the commanding officer to entertain his guests. (DS9: "Return to Grace")
Chain of command
The term "commmanding officer" can also be used to refer to the officer whom one directly reports to in the chain of command within the same division, or simply identifies an officer of higher rank in comparison to another.
Lieutenant Commander Geordi La Forge once referred to himself as the commanding officer of Lieutenant Reginald Barclay. (TNG: "Hollow Pursuits")
Commander William T. Riker was adamant about following the orders of one's commanding officer when confronting his transporter duplicate Thomas Riker. (TNG: "Second Chances")
The Romulan defector "Setal" admitted to William Riker that his commanding officer was Admiral Alidar Jarok. (TNG: "The Defector")
Worf acknowledged the fact that Riker was his commanding officer before the latter agreed to the former joining him on an "unannounced visit" to the J'naii planet. (TNG: "The Outcast")
Riker again brought up the issue of one's commanding officer when he, under threats by Arctus Baran, demanded that Data withdraw the USS Enterprise-D from their attempt to stop Baran's mercenary ship. (TNG: "Gambit, Part I")