In the simplest possible terms, what we do is study and practice sword-fighting.

Classical fencing is simply the proper use of a sword -- as if it were sharp!

Classical fencing is the use of the sword in accordance with its function, in a manner that optimizes the user's chances for survival in a "courteous and frank encounter" that is, in a duel.
The tactical, strategic, and psychological principles involved are applicable to a wide range of situations. 

Because we are inundated with misinformation about the sword and its use, it may be helpful to describe what classical fencing is not.

Classical fencing is not connected to a particular historical period, or to a particular historical fencing master, or "style," or to a particular weapon. We practice longsword, rapier and dagger, sabre (mounted and dismounted) and smallsword. 

Classical fencing is not  sport, not stage combat, not fantasy role-playing. We are not "re-enacting" or "interpreting" some obsolete ancient practice, any more than today's carpenter is "re-enacting" some ancient art when he/she uses a hammer, or any more than today's musician is "re-enacting" when he/she plays a piece written by Bach. 

 Like classical music, classical fencing strives toward a particular ideal of "poise, balance, proportion, simplicity, formal discipline, craftmanship, and universal and objective (rather than idiosyncratic and subjective) expression," affording us a "standard or model of excellence that has enduring value."