As far as I know there is no proved scientific approach that explains, how we sense someone is looking at us from behind. Brain in a way perceives the situation and can react (turn toward who is looking at us), but it is not that the brain do anything, it is only the result of the perception.

Public_speaking
First we should consider that the attention plays a very important role in people’s life, speaking in public could be as addictive as skydiving, however what they receive is only attention from others.
Lot of people in community are fighting for attention, sure you know a lot of attitudinizing people in your environment.

how-your-press-release-grab-attention

In some of the books the phenomena “attracting attention” is described as part of the human nature. There are several tactics – that also could be identified in your personal life -, how we attract attention from others, like “poor me”, “play coy”, “threat others”, “judging and questioning”. These dramas are so natural for us, that we even does not realize we follow one these, but this strengthens the fact attention is very important for people.

You sense the attention, not at physical level like a touch, it is much smaller piece of information, but it exists. Imagine that you can change the behavior of an electron  just by paying attention on the observation (experiments in quantum physics proved this statement). Using this analog with the same attention you can change the state of particles in others, which means the body has the possibility to sense. In everyday it just happens, it is not your thoughts or your brain produce this.