In a criminal profile, the unsub (short for unknown subject or unidentified subject of an investigation) is the unidentified person whose crimes are being investigated. The term "unsub" is associated with "unsub profiling," where investigators determine traits about an unsub to narrow the suspect pool.
An unsub is not the same thing as a suspect. A suspect's identity is known to investigators, whereas an unsub's identity is not; also, while an unsub is known to have committed the crime, a suspect is only suspected to be involved.
On Criminal Minds
On episodes of Criminal Minds, the BAU solves crimes by building a profile of the unsub, comparing suspects to the profile, and helping local law enforcement locate and apprehend them. As such, the unsub (or unsubs) is usually the antagonist of an episode, and their identity is usually not revealed until the BAU identifies them.
As revealed in the Season Thirteen episode "Believer," it is considered bad practice for an FBI investigator to give a nickname to an unidentified criminal, which is why generic terms like "unsub" are preferred.