Charged with possession of a firearm not in my possession. What's that about?

Firearm offenses can carry severe penalties and you need the assistance of an experienced criminal lawyer if you are facing charges or have been charged. 

It is not clear from your question where the firearm was found or located, but in criminal law, possession can be "actual" or "constructive" possession.  Actual possession  means you have immediate, direct and physical control of the firearm. It could be in your hand, a fanny pack you are wearing, or the pocket of your jacket. 

Constructive Possession on the otherhand turns on whether you have the power and intent to control a firearm, when that firearm is not actually on your person.  You can be liable for possession of a firearm when you constructively possess it, by for instance storing it in your home, or your car glove compartment, or some other location over which you have dominion and control, and there is evidence that you knew of the firearm's presence. Constructive possession may be found even where another person actually possesses the weapon, but you have the ability or intent to exercise control over it.

Constructive possession can be also be joint, such as when the firearm is found in the living room (common area) of an apartment with multiple occupants.  The question comes down to access, control and knowledge.  The prosecutor must prove you actually knew the gun was there and had the intent and capability to exercise control over it.  There are no simple answers to the question of whether a person constructively possessed a weapon without a careful analysis of the facts and circumstances of the individual case.