Imagine living as a very relaxed, calm, chilled-out human in the times of our very distant ancestors, back when we were living in caves and were potential breakfast for other animals. So you would wake up feeling like today was going to be a good day, noticing the sunlight streaming prettily into your cave. Out you would go, with not a care in the world, ignoring the sounds in the surrounding bushes, assuming it was just the gentle breeze causing the leaves to rustle ever-so slightly. What could possibly go wrong on such a beautiful day? You are so very relaxed, enjoying the warm morning sun on your face, that you don’t notice the danger until it is too late.
Unfortunately, the fact that you were breakfast for a sabre-toothed tiger has meant that you didn’t survive to pass on your genes. Your twitchy, nervous neighbour however, who is constantly on the high alert for threats and dangers, has a cave-full of equally jumpy, anxious offspring. 
Back then, being hypervigilant for potential threats, dangers or problems was important for the survival of our species. However, now we live in the modern day, feeling constantly over-alert and over-sensitive (both to our external world and to our inner thoughts and bodily sensations) causes significant problems for some people. It can feel like living with a faulty mental and emotional alarm which is constantly going off, even when there is no actual threat or danger. More often than not, in the modern day we are more afraid of our own imaginations than the reality of any given situation.
Hypervigilance is a potentially very damaging unhelpful thinking style as it can lead to feeling almost constantly stressed: it is hard to relax when you are always looking out for things to worry about. Also, when we are intent on searching for problems, it is highly likely that we will find or create them.
Hypervigilance is usually the result of a cocktail of other unhelpful thinking styles: worrying, being catastrophic/over-dramatic and negative thinking all contribute to hypervigilance. This can lead to a very unhelpful cycle of behaviour where:
1) You pick up negatively on everything around you (or within you)
2) You blow it up into a bigger “danger” (catastrophise it) 
3) You therefore have the stress response in response to the “danger” which leads to tunnel vision and increased focus for threats
4) You become even more focused on and sensitive to looking for potential threats.
And so the cycle continues, maintaining the hypervigilance.
It is very hard to keep life in perspective when you are always on the look out for problems. It also means that when a hypervigilant person is in a situation that they perceive as threatening, they are so focused on it, they forget about (or can’t connect back to) previous similar past experiences where it turned out to be okay and they actually DID cope, so they are unable to calm themselves down in the moment. Some people permanently live this way, where it has become normal for them to habitually be stressed.
We are not designed to live in an almost permanent state of stress arousal and the end result can be psychological issues, for example social anxiety, health anxiety and phobias such as emetophobia (a severe phobia of vomit/vomiting) as well as other mental health issues. It can also lead to physical health problems because prolonged stress can affect the immune system.