At some point during the Rebellion, Homeworld Gems no longer saw Earth as a viable colony. Instead of exploiting the planet for its resources like originally intended, Homeworld Gems planned on planting a geo-weapon inside Earth itself with the intent of destroying the planet and any remnants of the Crystal Gems.
These early experiments only combine two or three shards. The Cluster will be a billion times bigger. An inseparable fusion capable of destroying worlds, starting with this one.
—- Peridot, "Gem Drill"
The shards of fallen Gems from the ongoing war were collected by Homeworld Gems and experimented upon, forcibly fusing the shards together into Cluster Gems. Once enough experimentation was completed, Homeworld Gems fused together millions of Gem shards. This massive assortment of Gems was then planted into the Earth's mantle at the Beta Kindergarten. When this beast, known as the Cluster, takes on its physical form, it will be much bigger than the Earth itself, completely ripping the planet apart inside-out. As implied by Yellow Diamond and Peridot, Homeworld can then use the Cluster as a weapon to destroy other worlds.
The Cluster being an aggregation of many gem shards means that its personality can be likened to a hive mind. They seem to retain some consciousnesses as a collective, however, as Steven's actions in "Gem Drill" make it bubble itself. This is further shown in "Reunited", where the Cluster behaves as a single entity and fights Yellow Diamond's Ship on its own, recognizing Steven and giving him a thumbs up.
Look, I know you're scared, but I'm not going to hurt you. And whatever's going on, whatever the Cluster is, I wanna help.
—Steven, "Catch and Release"
Details were later mentioned in "Catch and Release", when Peridot was cornered and finally captured by the Crystal Gems. When Steven released her, she reveals that the "emergence" of the Cluster would be a catastrophic event that would destroy everything on Earth.
Peridot explains that after Homeworld no longer saw Earth as a viable colony to mass-incubate Gems, they started doing experiments with the Gem shards, fusing them together to create an artificial fusion as a type of "Gem geo-weapon". She reveals in the Prime Kindergarten Control Room that the forced Gem fusions they were fighting were prototypes for the Cluster, a giant forced Gem fusion at the core of Earth composed of millions of Gem shards. She mentioned that it would be much bigger than Earth if it emerges and takes its physical form, and will destroy the planet once it does so.
This is the Cluster. A massive, artificial fusion composed of millions of Gem shards. It has laid dormant for thousands of years within this planet's crust. When this Gem activates and takes its form, the result will be catastrophic.
—Peridot, "Back to the Barn"
Peridot mentions the Cluster to the Crystal Gems, revealing the details of what the Cluster actually is. The Crystal Gems then decided to build a drill and try to reach the Cluster before it gets to the end of its incubation period.
Gotta find the right file... aha! Cluster, Cluster, where are you, Cluster? Aha! There's the insertion point. Looks like the Beta Kindergarten in Facet Nine. It's the smaller of the two, not nearly as impressive as yours, Amethyst.
—Peridot, "It Could've Been Great"
Peridot reveals the Cluster's location through the Diamonds' computer in the Moon Base. As shown, it is located beneath the Beta Kindergarten, and was embedded deep in the mantle approximately 2,500 units down relative to the Barn.
But the Diamonds are bad! They don't care about the Earth! They wanted to hollow it out, and now they wanna blow it up with the Cluster!
—Steven, "Message Received"
After embezzling the Diamond Communicator, Peridot argues with Yellow Diamond to terminate the Cluster so that they would not sacrifice the organic life for such a Gem geo-weapon. Yellow Diamond replies, "I want my Cluster, and I want that planet to die. Just make that happen." She also orders Peridot to let the Cluster grow undisturbed.
The ground shook. This could be the start of the emergence of the Cluster. Stage 1: Slight tremors every quarter hour. Stage 2: Full scale earthquakes. Stage 3: the Earth is destroyed! We're running out of time. We need to drill right now!
—Peridot, "Super Watermelon Island"
The Cluster tries to emerge in this episode and causes some tremors. Peridot recognizes these tremors and says that the Cluster is causing them, but the other Gems believe that Malachite is causing them. After they defeat Malachite and force her to unfuse, the Cluster causes an earthquake on Mask Island, which results in Jasper falling into a fissure.
Ugh! Am I the only one who understands the meaning of teamwork?! Okay, Steven, are you ready to drill down into the planet to depths never before reached by your species to stop the Cluster before it forms and save your world?!
—Peridot, "Gem Drill"
Earthquakes begin rocking Beach City, indicating that the Cluster is only hours away from taking form. Steven and Peridot drill deep into the Earth where the Cluster is located but are unable to pierce the surface of it. As Peridot tries to destroy it, Steven sees faces and hears the voices of the Gem shards comprising the Cluster, and starts to talk to it as he falls unconscious. He convinces it not to form and, instead, to bond with itself. The Cluster begins to take form uncontrollably, however, so Steven attempts to bubble all the Gem shards. He eventually wakes up and notices the Gem shards inside the Cluster are bubbling each other. Steven finishes it off and merges all the small bubbles into one immense bubble, completely encasing the Cluster and preventing it from destroying the Earth.
Yellow and Blue Diamond arrive on Earth and awaken the Cluster. Its bubble is popped, and it forms. However, instead of going on a rampage, it sides with the Crystal Gems, and fights Yellow Diamond's ship in the form of a giant arm. After both Diamond warships are destroyed, the Cluster returns to the core of the Earth, and presumably bubbles itself again.
The Cluster is an immensely powerful geo-weapon designed to obliterate whole planets. The simple act of taking form would result in the destruction of the Earth, after which it would be used to devastate other planets. Unlike other fusion experiments, the Cluster has achieved a degree of control over itself. Its gemstone is immensely durable, withstanding penetration from a drill that could effortlessly pierce several strata of the Earth's crust and mantle.
Its nature as an artificial fusion of millions of Gem shards grants it many unique properties. It is the only known Gem to be able to create bubbles before taking form, and to remain sentient and able to converse with itself while itself in a bubble.
Partial Formation: In "Reunited", the Cluster demonstrated that it can form as only a minuscule fraction of what its actual size is supposed to be, in order to avoid destroying the Earth. When it did so, the portion of it that emerged from the planet's crust in the form of a massive arm was roughly the size of a Diamond's ship. This form is not sustainable, as shown when it began to be destabilized after the fight. The Cluster can voluntarily dispel it at any given time.
Extrasensory Awareness: The Cluster's arm was able to precisely interact with its surroundings and with Steven without possessing any visible sensory organ.
Immense Strength: When it manifested as an arm, the Cluster punched through all layers of metal and rock between its location and the Earth's surface in mere seconds, and before taking form. Later, it was able to block Yellow Diamond's Ship when it tried to ram into it before matching and eventually overpowering it, also crushing Blue Diamond's Ship in the process.
Peridot refers to the Cluster as a "Gem geo-weapon". This is a play on the term "Bioweapon", Bio- referring to organic life while Geo- referring to rocks and minerals. This is appropriate, seeing as how Gems are a race of sentient gemstones and are thus inorganic.
In "Back to the Barn", Peridot was convinced that the Cluster lay exactly at the center of the Earth. It is only in "It Could've Been Great" that the correct location of the Cluster was discovered. This could be due to Homeworld being unable to implant it at originally planned due to the rebellion and the records failing to reflect that, or simply a retcon.
Unlike Gem mutants, when the Cluster attempts to reform, its appendages are translucent.
Also, unlike Gem mutants, it possesses a rudimentary intelligence — likely because of a hive mind formed from the shattered intellect of the millions of shards that compose it.
The Cluster's gemstone bears a strong resemblance to an Angel Aura Geode, while its physical form shares strong similarities to the musclular system of a human arm.
Whenever the hand of the Cluster loses control of its physical form, it makes the same sound that Amethyst did when she "glitched" for a few seconds periodically during the time she was cracked.
The Cluster bears a great resemblance to Lavos, the main antagonist of the Chrono Trigger video game. They are both extraterrestrial creatures that will initiate an apocalyptic event if they are released/awakened unless a group of heroes stops them.
The Cluster's theoretical shape.
Steven's sock puppet interpretation of the Cluster.