Extrasensory perception (Chōkankakutekichikaku) (ESP) in the Toaru Majutsu no Index universe is one of two criterias that esper powers are grouped into, the other being PK or Psychokinesis.
Basically, ESP involves reception of information not gained through the recognized physical senses but senses with the mind. Powers that allows one to learn of distant or future scenes are classified in ESP, like Precognition. As explained by Tsukuyomi Komoe, ESP has a lower precedence in classification of esper powers than PK, especially when an esper power sits on both sides of the boundary between ESP and PK.
When we are aware of ourselves and of others who are in our daily life we become linked by a common bond of social interaction that binds society together in compassion and overlapping needs. But a sense that goes beyond this is to be aware of the universe outside of ourselves to perceive the flow of psychic currents and by this means gain the ability to interact with others and our environment. The so-called 'Sixth Sense' is really a complex assortment of different functional abilities that all rely upon the mind and spirit linking together. Learning to harness and channel this sense can make you truly formidable and a vastly more capable Man of Wisdom.
It is for this reason that this ability is often confused with Precognition by the science side. When in fact it is just a instinctual part of the human psyche that has nothing to do with either magic or esper abilities. As we get older we get weaker, both physically and mentally. That’s something we can’t avoid. But there’s one thing we can do. Something we can keep getting better at until the day we die. In the wild where survival of the fittest is law herbivores never lay down to rest for just a moment of carelessness can spell death. At midnight they must remain alert for any sights sounds or smells of their predator's movements. Every day requires the utmost attention in order to sense their enemies.
By repeatedly escaping from enemy threats their survival has enabled them to refine their 5 senses to the extreme giving birth to a new 6th sense one that can sense the approach of death. A lone elderly zebra was too weak to run any longer. But it was clearly able to tell what was in its surroundings. It lived its days in peace amidst this dangerous savanna for this zebra was able to sense within a 2 kilometer radius the location of all its predators. Humans have this sense as well however through centuries of disuse it has become stagnant only surfacing during times of great stress.
The harsh training martial arts put themselves through allows them to reawaken this sense allowing them to see things without relying on their eyes. It’s like the fighter is standing in a pond of water or on a spider's web. The moment a person steps into that pond or on that web, the fighter is alerted due to the ripples (pool) or vibrations (web) created. The more skill the fighter gains the bigger the pool gets. Only other master warrior samurai and newborn babies can enter this field without being noticed by the fighter. Try as you might if you don’t have the sixth sense you can be one of the best, but you’ll never be number one.
The many fights Kamijou Touma has been in has cause him to develop this ability allowing him to subconsciously anticipate the attacks coming his way. Minute changes in the battlefield, like Mikoto exuding her electromagnetic field that makes metal items around her resonate, these involuntary movements of hers that not even she can detect, aid Touma in his judgment in where to put his Imagine Breaker. The narrative refers to such phenomena that Touma can be perceived by as "An Involuntary Movements", but implies that its scope differs to the term AIM, and most likely uses it in a literal sense, as in actions that are not voluntary in the part of one who is doing it, like blinking. Mikoto's railgun attack was over three times the speed of sound, and lightning strikes were even faster. Even with a method of defending himself, to be able to time it right was extremely difficult, missing the timing by only an instant would probably result in death.
Later when fighting Leivinia Birdway, she attacks Touma with countless daggers of water that are packed so fully that it leaves no space for him to hide or evade. But it does not work, for Touma negates a dagger, a dagger that would specifically cause all others to be thrown out of the way after breaking into pieces in a chain reaction that created a blank spot that should not have been there.
However as a regular street fighter with no actual training Touma has no idea how to properly utilize his sixth sense. This is seen whenever he tries to actively tries to take note of these things (referring to the information that he subconsciously takes in and react to) it doesn’t work. Another weakness that Touma has tdue to his lack of training is the fact that his sixth sense can be sealed by restricting the information that is shown to him. Rensa controls her cyborg body in such a way that she completely freezes her facial expression, prevents even the slightest involuntary muscle movements, and times her blinking and breathing to specific set intervals in such a way that Touma was not be able to 'read' her based on those things.