The Data Overmind, called the Data Integration Thought Entity in the anime (情報統合思念体 Johō Tōgō Shinen-Tai) is a conglomerate of the sentient data organisms which supervise the part of the galaxy in which Earth is in.
It is divided into five or more factions—Moderates, the Innovative, the Compromise, the Thinking party and the radical faction—which do not necessarily agree or even cooperate with each other on basic goals. In The Surprise, Ryoko Asakura said the entity was controlled by a consensus of conservatives "always trying to preserve the status quo".
It seeks to auto-evolve itself, and holds humanity in general, and Haruhi Suzumiya in particular, as the key to this.
Kyon is not fond of the Data Overmind, partly because of its indifference to Yuki Nagato's condition (it considered punishing Yuki for her actions in The Disappearance, and showed indifference to her illness in The Surprise).
The Data Overmind is supposedly as old as the universe itself.
The Data Overmind noticed numerous biological creatures that had reached a level of self-awareness, but of these creatures humans were the first to reach a higher level of intelligence.
It became aware of Haruhi when she unleashed a massive data flare on Tanabata, year 0. The Data Overmind can modify but not create data, and believes this ability to create data is crucial for its auto-evolution.
The Data Overmind is incapable of communicating directly with humans, since it is an Astral being as stated by Nagato. It created a variety of Humanoid Interfaces, referred to as TFEIs, in order to facilitate communication with humans as it does not communicate through language. There are "many" on Earth, and the currently-seen examples have different personality profiles. TFEIs can only relay information from their own faction.
It looks forward to seeing changes in their observation subject, but different factions have different ideas about whether such changes should be provoked. Ryouko Asakura of the radical faction wants (or wanted) to kill Kyon to get a reaction from Haruhi.
During The Disappearance, when Yuki altered the world, the Data Overmind did not exist during that timeframe.
Interactions with the Sky Canopy Dominion
The Data Overmind has limited interaction with another data entity, the Sky Canopy Dominion, described by Yuki as a "similar but separate" entity which exists in a different "place". There hadn't been any contact, because they felt that contact would not lead to any mutual understanding. Like the Data Overmind, it was interested in Suzumiya.
By The Disappearance the Sky Canopy Dominion had created a humanoid interface, Kuyou Suou. The interface attempted to locate Kyon but mistook Taniguchi for him instead, and began dating him. Nagato may have played a role in this confusion. When Nagato recreated the world at that time, the Sky Canopy interface was unaffected.
The first interaction with the SOS Brigade occurred in Snow Mountain Syndrome, where the Dominion, in an attempt to learn about Yuki, placed her and the rest of the SOS Brigade into a scenario where Yuki could not use her powers to escape. In response, the Data Overmind caused her to fall "ill" so she would not understand what the Data Overmind was trying to convey. This prevented the Dominion from learning from her.
Nagato met Kuyou Suou at an impromptu meeting. The two attempted to communicate, but not only was the level of communication minimal, the Data Overmind's response eventually resulted in her "illness".
Yuki noted that it had taken quite a long time (based on the limited communication in that incident) for the Data Overmind to even learn the Dominion's name. (The entity had previously named it the "Macrospatial Quantum Cosmic Existence").
She believed they could create a humanoid interface and then learn about Haruhi, or even communicate with other interfaces through speech.
Later Ryoko Asakura was dispatched to prevent Kuyou Suou from approaching Kyon. Meanwhile, it's attempts to communicate with Yuki rendered her "ill" again.
Following the closed space confrontation, Nagato was removed from her post facilitating communication between the Data Overmind and Sky Canopy Domain as the level of communication that could be sustained was insufficient. Nagato's new task was to observe Haruhi Suzumiya and Kuyou Suou.
Meanwhile, Kuyou Suou adopted the goal of achieving autonomy for herself.