Some of the cases handled on the show are based on real life serial killers. But the representation of behavioral analysts in the show is a lot more exciting than it actually is in real life. The FBI behavioral analysts have to do a lot more work, and they walk a path much harder than what the show portrays.
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.