Extrasensory Perception

Extrasensory perception (超感覚的知覚) (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.

Terminology
The English Toaru fandom uses the term "esper" (derived from ESP) as the translation for the participants of Academy City's Power Curriculum Program, despite that many esper powers are not classified as ESP type powers.

Principles
Extrasensory Perception or ESP, is a category of esper powers which refers to abilities that function on the principles of using the mind to receive sensory information through means other than the five known senses of the human body. Esper abilities that enable their user the to receive knowledge of remote or past/future events are commonly classified as ESP type powers (such as 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. For example, Thoughtography may seem as though it would be categorized under ESP as a power which allows one to learn of distant and future scenes, however the power which affects the film is a physical one so it is a power which influences an external object, hence it is classified under PK.