The Shaper of Worlds originated as a Cosmic Cube, developed by the Skrull Empire long before humanity evolved. The Skrull Emperor wanted to use the Cube to enforce his rule as God-King. However, the Cube eventually rebelled against the Skrull Emperor because of the ambitious and aggressive nature of the emperor's mind imprinted on it. It developed sentience, and became the Shaper of Worlds. In retaliation to the Emperor's actions, the Shaper of Worlds wiped out two-thirds of the Andromeda Galaxy, leaving the Skrull Empire in ruins for thousands of years. The Shaper of Worlds changed his form into a half Skrull and half robotic being.
He spent much of his time manipulating worlds throughout the universe. During this time he tutored Glorian.
Much later, after communicating with the Kree's Supreme Intelligence, which was keeping track of the universe's Cosmic Cubes, the Shaper of Worlds found the A.I.M. Cosmic Cube just as it was about to develop its own sentience. It was also wrestling with the negative emotions of its users, but the Shaper managed to calm it down. It took the Cube with it, and began to teach it how to be an "adult" Cube. This new Cube became Kubik.
At one point, Dr. Doom and the Fantastic Four entered the Beyond-realm where the Beyonder lived. The Shaper and Kubik showed up and tried to stop Doom's plan (which would have ultimately given him the Beyonder's power). The Beyonder tried to battle them but found that he could not defeat them. Then the Molecule Man showed up. Kubik and the Shaper explained that the Beyonder and the Molecule Man's power came from an aborted Cosmic Cube, and helped them merge their power together to form the Cube they had always been meant to be. When this Cube became sentient, and took the name Kosmos, Kubik took over the role of mentoring it, thereby fulfilling the Shaper's original plan for making sure that any new Cubes had a better "childhood" than he did at the hands of the Skrull Emperor. (Unfortunately this did not work out very well, as Kosmos eventually turned herself into the Maker, went insane, and was killed.)
He is noted in a recently compiled Skrull Handbook that was sent to Queen Veranke as being potentially loyal to Earth and is perhaps still harboring ill-will towards The Skrulls. It was also said that if this was the case Veranke should not attempt to seek him out and that he should be left to his own devices.
The Shaper is, as Kubik called all the sentient Cubes, a "minor omnipotent." He has extensive matter and energy manipulation powers. For instance, after a Cosmic Cube altered the entire Earth into a Technopolis, he was able to change it back with a wave of his hand. The exact limits of a sentient cube's powers are unknown, but can be presumd to be approximately the same as a Cosmic Cube's. Kubik once said they were less powerful than the Celestials.
Cosmic Cubes are created in the first place by sending energy from the realm of the Beyonders (plural) into our universe. The Beyonders are interested in matters of evolution and development, so the development of the Cubes into sentient beings is part of their overall experiment with our universe.
Some other examples of the powers of sentient Cubes can be found in the Kubik and Kosmos entries.
On Earth-1720 (the home reality of Susan Storm a.k.a. Madame Hydra) The Shaper of Worlds is known as The Maker and unlike his counterpart who was originally just Cosmic Cube, The Maker actually originated from a species of Makers. However due to his violent nature and his all-consuming desire to create as much Chaos as he possibly can wherever he goes he has become a pariah amongst his people. When he attacked Earth after gathering the five most dangerous villains on Earth (save Madame Hydra who was in another reality), The Maker was confronted by The Exiles and the Valeria Richards of Earth-1720. His attacks caused Proteus to emerge from deep within Morph's subconscious mind and shortly after being released The Maker was beaten into submission.