I’m not qualified to go into detail, someone else might be able to help out. But the basics are that we rely on pattern recognition for survival. We recognise that the sun comes up every day and sets every evening, our daily life is based around this pattern (a legitimate pattern.) We get stung by a bee more than once and we learn to stay away from bees. Everything we learn is based on pattern recognition. The down side to this is that we tend to see patterns where there are none, and we also put meaning to patterns that have no meaning.
You’re still looking for patterns, you’ve just narrowed down what patterns you consider to be significant. That doesn’t mean your refined patterns really are significant though.
“Looking for” is possibly too strong a term. You aren’t necessarily consciously looking for patterns, but your brain is designed to recognise them, even when you aren’t looking for them, so they “jump out” at you. Once you note the beginnings of a pattern, you take even more note of other details that fit the pattern, and you subconsciously discard information that doesn’t fit the pattern.
The train of logic goes like this. As per my example, people tend to make their experiences fit into their world view (the negative person percieves neutral experiences as negative, the positive person percieves the same neutral experiences as positive.) So then, someone who believes that psychic phenomona exist, will see a series of coincidences as evidence of psychic phenomona, even if it isn’t. Someone else, who feels that psychic phenomona doesn’t exist, will see the same series of coincidences as an interesting collection of random events.
When you write a novel and then find some startling connections with someone else poem, you naturally consider it to be evidence of some kind of psychic ability, even though it may not be (and IMO, probably isn’t.)
Another good example of this is when the devoutly religious see images of religious figures, such as Jesus, in clouds, stains on a window, or even in a slice of toast. Their brain picks up on patterns that fit with their own perception of the world. I’d probably look at the same clouds, stains, or piece of toast and see pictures of dogs and aeroplanes. Both of these interpretations are equally (in)valid.
As far as the sensations go. We all experience interesting feelings when unusual things happen. I think most people have had the hairs on their body standup, the skin on their head crawl, and felt a strange “expanding-of-horizons” sensation when confronted with an unusual experience (a good movie can evoke this kind of emotional response.) Now I’m not saying this is the same feeling that you have when you see a particularly compelling connection, what I am saying is that the body and mind can respond in unusual ways to what are, essentially, mundane experiences. Just because you feel like something incredible has happened, doesn’t mean it has.
By “nothing special happens”, I mean nothing that appears to be a psychic event. Obviously special things happen to people all the time. I have a fantastic life, everyday I generally have some thought along the lines of “wow, here I am, isn’t this good?” But it’s due to fairly mundane things like my relationship with my wife, my daughter, my job satisfaction etc. I think that the world and universe, as currently understood, is a pretty special place.
As others have said, I’d be even more impressed if some kind of psychic ability was shown to exist, unfortunately, I don’t believe that any of the evidence for it is convincing.