This is something that's a trope in writing, and I've heard people talk about it. I'm not sure I've ever felt it!
I can think of three likely possibilities:
- subconsciously noticing the direction of people's gaze through cues that come across as a feeling rather than a visual thing. This would seem to preclude a couple common experiences, though - "I felt his eyes drilling into my back as I walked up the stairs", or "The place was abandoned, but nevertheless I had the feeling of being watched"
- being self-conscious of your appearance or some aspect, or of being in a place or doing an action that makes you embarrassed or wary. This is the thing that I think I've felt, but properly would be used to indicate the subject's mental state rather than the actions of others (which often seems to be indicated when people say this)
- some actual physically-explainable detection of sight on our bodies. I find this to be a stretch for obvious reasons, but maybe there's something I haven't thought of
Can you feel eyes crawling over your skin? Someone checking out your ass as you bend over? Can you feel the weight of the crowd's gaze as you step on stage? How?