Haruhi's near-omnipotent abilities; which have led to the members of the fandom jokingly being referred to as followers of "Haruhiism", allow her to subconsciously change, destroy, or likewise alter reality based on her inner hopes and desires. Her strange abilities have led to various characters in the series referring to her in different ways. Yuki states that the Data Overmind refers to her as "the potential for auto-evolution", Mikuru says that the people of the future believe that she is the originator of a large time-quake that has forever altered the space-time continuum, and Itsuki claims that the Agency has declared her to be God.
These differences in opinion stem from a massive and spontaneous universal event that occurred three years prior to Haruhi meeting Kyon, of which Haruhi is said to be the cause. The event attracted the attention of three prominent recurring groups: the Data Overmind, time travelers from a distant future, and a group of espers known as the "Agency" (or the "Organization", according to the English anime adaption).
Her powers are triggered by her emotions and inner desires. Whenever she becomes emotionally unstable she subconsiously creates patches of dimensional space; referred to as "closed space", where-in gigantic energy beings destroy the cityscape to vent out her frustrations. It has been theorized by the espers that the current universe may just be one in a string that Haruhi has subconsciously created, as; despite having these powers, Haruhi is completely oblivious to them or the existence of aliens, time travelers, and espers.
All three of the other members of the SOS Brigade have; at one point or another, stated that Haruhi "chose" Kyon. She often trusts Kyon, believing him to be capable of dealing with anything. Kyon is the only person whom she has been truly open with, and when she briefly created a new world he was the only person from the original world that she had believed was worth taking there completely unchanged. This is made even more evident in the fourth novel and in the animated film; The Disappearance of Haruhi Suzumiya, where she remained at Kyon's bedside for the three days that he was in a coma due to an accident.
Read more about this topic: Haruhi Suzumiya (character)