Originally the Infinity Man wasn't given a concrete backstory and was implied both to possibly be a combination of the powers of the Forever People through their Mother Box or an avatar of the Source.
When the more mysterious backstories of the Fourth World were explored, it was revealed that the Infinity Man had originally been Drax, son of the Queen of Apokolips Heggra and the brother of Uxas. Drax took on the role of Infinity Man after being betrayed and left for dead by Uxas. He formed an alliance with his old friend Izaya, now the Highfather of New Genesis, and became the protector of the Forever People.
Following the rebirth of the New Gods in Final Crisis and the Flashpoint reboot, he was given a new origin.
Infinity Man was created when the young Highfather travelled to the Source Shard seeking a way to defeat Darkseid's war machines without trading his son to Apokolips. Infinity Man was split from Highfather as he railed against the Source, created to contain Highfather's conscience, his memories of his lost wife Avia, and his compassion, so that Highfather could do what he felt he had to do to save his people.
Infinity Man was created by Jack Kirby. He was rebooted by Dan DiDio, Keith Giffen, and Tom Grummett.
In the Bronze Age, the title of Infinity Man was described as a legacy, originally belonging to a man named Astorr. A warrior from a distant planet, he stumbled across the broken and burned body of the young New God named Drax, the brother of Darkseid, who had been horribly injured in his quest for the Omega Force. Nursing the young man back to health, Astorr passed on the identity of Infinity Man shortly before dying of old age. Taking up the identity, Drax became a warrior for Highfather of New Genesis. It was presumably during this time that he met the Forever People, for whom he would later act as protector. The exact nature of their relationship, and why precisely he was always willing to fight their battles, goes largely unexplained, save by vague hints at an "arrangement". Eventually his brother grew wary of the threat posed by Infinity Man, and imprisoned him in another dimension, leaving him stranded on the distant planet of Adon, which he could only escape by trading places with the Forever People.
The New 52 introduced his current origin and powers. Notably, he is no longer related to Darkseid, and is instead a fragment of Highfather.
Major Story Arcs
The Forever People
Throughout the Forever People's self-titled series, he acts as their protector, frequently aiding them in battle as their main offensive weapon. In one such battle he fights Devilance the Pursuer on an island in the Pacific Ocean. The fight results in both being apparently destroyed, along with the island upon which the fought. Though apparently dead, he eventually returns to life.
Countdown and the Death of the New Gods
During the Countdown to Infinite Crisis, Infinity Man is suspected by some of being responsible for the deaths of a number of New Gods, including the Forever People. He is eventually revealed to have been responsible, disguising himself as Himon in an attempt to mask his involvement. His motive is unclear, but presumed to be related to instructions received from the Source, which he claims as a motive. Using the souls collected from the New Gods he creates another Source Wall that surrounds the original. He ultimately battles Mister Miracle, who has been empowered by the Anti-Life Equation, near the Source Wall. The destruction of the second Source Wall during the fight leads to the reuniting of the Source and the Anti-Life Equation, which are revealed to be two halves of a long-separated whole. Infinity Man is apparently killed in the battle.
Infinity Man and the Forever People
Split from Izaya, Infinity Man grows increasingly troubled by the dangerous decisions being made on New Genesis and Apokolips, and the destabilizing effect they have on the universe. He contacts the Forever People through their Mother Box, and begins to merge with them against their will during their humanitarian mission to Earth. He attempts to shape their paths so that they will reunite him and Highfather.
A version of Infinity Man appears in the Amalgam Universe, as a member of the Un-People, a team created by the amalgamation of the Forever People and the Inhumans. This version of the character was called Infinity, the Beta-Ray Man, and was an amalgamation of Infinity Man and Beta Ray Bill.
A version of Infinity Man appears briefly in this Elseworlds story.
Powers and Abilities
Infinity Man appears to have some manner of direct connection to the Source. Because of this, he displays an extremely wide array of powers, the expression of which seem to be at least in part influenced by who is involved in summoning him. More commonly displayed powers include superhuman strength, flight, phasing, and the use of Infinity-Beams. He has also displayed magnetokinesis, super speed, teleportation, matter manipulation, super endurance, healing, energy projection, telekinesis and telepathy. He can be summoned by the Forever People when they gather around their Mother Box and say the word "taaru."
Infinity Man appears in the Young Justice episode "Disordered". He does not speak in his appearance, and, contrary to his comic book counterpart, is apparently some form of mechasuit or robot who is created when the Forever People merge with each other and the Source, becoming more than the sum of their parts. During the episode a Father Box is used to briefly take over his mind and force him to work for Desaad.