Over the years of your life, you accumulate knowledge as to what is normal and what it not. The vast majority of this knowledge is accessed below the conscious level, meaning that your brain is processing information constantly without yourself being aware of it. Things, situations, scenarios in everyday life jive (clinical term) with what your brain has learned is normal or they don’t.
Often, people have a confirmation bias. “I had this feeling and it was true!” Often, your nerves interfere and you sort of force a perception that is unfounded.
When you listen to interviews of people who are on the periphery of a crime, witnesses of some kind, often there will be a pattern of “something not being right”, with a person of interest. Often, these are isolated, completely separate people.
Your brain picks up on cues as to behavior, facial expressions, moods of people, things said out of character and such.
Getting a “feeling of being watched” means that your brain senses something out of place even though your conscious isn’t registering it. It isn’t magic, nor foolproof, nor does it always mean there is a serial- torturing- satanic- rapist stalking you, it means that you picked up on something other than normal.