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.

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.

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

Principles
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.