The Incubators are a race of extraterrestrial aliens who grant one wish for girls with magical potential, in exchange turning them into Magical Girls. Their ultimate goal is to combat the universe's entropy levels.
As prepubescent human girls have proven to be the best source of energy available, the histories of Incubators and humans have been intricately linked. It has been implied that human innovation and technology have advanced so far and so fast only because they have been spurred on by the wishes made by girls throughout the ages.
The earliest suspected interaction between girl and Incubator is the discovery of fire.
The details of their technology and its relation with magic are not wholly understood (even to the Incubators themselves, when regarding magic). However, it is known that they harness the emotional energy generated by prepubescent human girls when they are converted into Magical Girls, and that they grant one wish or one "miracle" in return. They are also tasked with consuming Grief Cube, preferably saturated ones, in order to make sure demons do not spawn.
Incubators, before the formation of MSY, approached girls with potential on their own to pitch their offers, relying on two main sales points: the ability to grant one "miracle" of any kind (within reach of the girl's own "karmic destiny") and what girls as a whole would consider to be a "cute" appearance. They are responsible for explaining all aspects of a Magical Girl, including powers, conditions, and responsibilities, and especially including the fact that a Magical Girl's soul is transferred to her Soul Gem. Other than this, however, an Incubator is free to pursue a contract in any way they please, such as but not limited to gaining a position of trust by being sympathetic and urging on on the teenage impulses of potential contractees. There have been hints that Incubators deliberately engineered a situation that would force someone to become a Magical Girl, in the past. Most of these methods have, by this point, are now the responsibilities of the MSY and have been toned down.
Traditionally the Incubators had taught, guided, and coordinated Magical Girls when there were no tutors to do so, attempting to prolong each girl's lives as long as possible. They are ordinarily neutral in conflicts between Magical Girls, as their objective is to efficiently retrieve as much emotional energy as possible with concern for little else (though a notable exception would be Mikuni Oriko and her group, considering their efficiency in killing other Magical Girls). Since the advent of the MSY the Incubators often work in concert with them, as their presence have been shown to have extremely positive effects on MG longevity as well as a positive correlation with recruitment numbers.
 Physiology and Abilities
Incubators resemble white cats with long, floppy ears, each encircled by a golden ring. They have a teardrop-shaped mark on their back that opens to allow for consumption of Grief Cubes. The texture of their bodies and the consistency of their biological makeup are, presumably, similar to cotton plushies. Though they may eat regular food with the mouth on their face, it is unknown if it has any nutritious or otherwise significant value to them.
Only magical girls and potential magical girls can see or detect Incubators presence in any way, though whether this is the Incubators' natural feature or if they chose to largely conceal their presence is not clear. Incubators only communicates telepathically, and can act as relays for girls who are not Magical Girls yet (though they have never described if this ability works by "forwarding" a mental thought or simply mimicking and resending it).
Incubators are by nature emotionless, and views any hint of such on their kind as a mental disorder. Though Incubators told very little to humans about themselves, there are some suggestions that Incubator society operates on Governance's "Emergency Mode Level Four": the "mechanization of all human interaction".
 Reception by Society
In general, younger Magical Girls view and treat Incubators as the traditional, cute and cuddly Mahou Shoujo anime mascots. Karina Schei and Shen Xiao Long even teases Kyubey in jest, on one occasion. Older Magical Girls appear to be more aware of the Incubators' ability to manipulate.
Reception from the general population is less clear. It is known that the radically conservative sectors equates them to traditional demons, reminiscent of the saying "a deal with the devil". Youths appear more likely to respond to them with curiosity, if the sales of Incubator plushies are anything to go by. Parents most likely categorizes them similarly to MGs in general; grateful in public, yet spiteful where their girl is concerned. Scientists may or may not be frustrated by the lack of information on Incubators themselves and their technologies, or ecstatic in whatever furthering of sciences that they do offer. Military personnel and Governance are, presumably, gratified for the providence of Magical Girls.
Kyubey (キュゥべえ, Kyuubee) is the Incubator that featured prominently in the original series, being responsible for Mitakihara City. As such, he has an illustrious list of contractees to his name, including all three of the main protagonists, Akemi Homura, large parts of Ryouko's family, and, though he doesn't know, the Goddess herself.
Kyubey, for some reason, appear to be attached to Mami, never failing to meet her whenever she arrives in Mitakihara City.