The alien race called the Taelons (or Companions, as they are called in early seasons) are bound together by a psychic link with all other Taelons at all times. This link is known as the Commonality. Relatively little is revealed about the Commonality, this is partly due to the subtle nuances of Taelon phrasing (rarely lying, but often only giving part of the truth), the difficultly in trying to explain such a concept in understandable language, the need to keep the deeply spiritual Taelons mysterious and alien.
The Commonality is not a group mind per se, Taelons have individual personalities and minds, and the Commonality is referred to as "collective sentience". While Taelons can, in some cases, detect lies or actions through the Commonality (as when Da'an discovers that Zo'or has murdered William Boone), the Commonality does not generally allow Taelons to read each others' minds.
Humans with significant psychic abilities have been able to touch the Commonality. Since the Taelons consider the Commonality sacred and pure, they have not responded well to what they perceive as a potential invasion.
In the third season episode "Time Bomb", Da'an implies that every Taelon who ever existed continues to exist within the Commonality. This implies that Taelons, who have a more tangible connection to their spirit selves, do continue to exist in some form, conscious or otherwise, after their physical bodies die.
Renee Palmer and Liam Kincaid refer to the Commonality as being a "virtual plane" upon which the Taelons commune. If a Taelon's connection to this plane is severed, then they revert to an "Atavus"; an ancient life-form from which the Taelons themselves evolved. This term is problematic, as the term has been applied to three visually distinct and separate species over the course of the series. The Atavus have active shaqarava an organ situated in the palm of the hand, which they use to drain life-force from any prey that they hunt. The Taelons do not consider anyone who has fallen from the Commonality to remain Taelon. Interestingly, the psychic link can be damaged or broken by technological interference, as shown when the computer genius Augur accidentally separates Da'an from his brethren. Active shaqarava are required to reconnect a Taelon's consciousness to the Commonality, therefore the Taelons are incapable of restoring the link, though a Kimera can do it.
In the fifth season, a single Taelon survives - Ra'jel. He does not degenerate into an atavistic state. He is said to be the first Taelon and the "sire of the Synod" (the Synod being the Taelon ruling body) and that he contains the entire Commonality of the Taelon race within him. As far as anything in the final season is implied, it is implied that, as the first Taelon, he is the only member of his species to have never needed other Taelons to bond with.
The future of the Commonality is uncertain, while it still exists, there is but a single Taelon left.