Puella Magi

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Puella Magi is the term for a girl who has made a contract with Kyubey, having a wish granted in exchange for magical powers and the responsibility to battle Witches.
Upon making a contract, a Puella Magi receives her Soul Gem, which acts as a conduit for her power. A Soul Gem darkens as the Puella exercises her powers and must be "cleaned" periodically using Grief Seeds, which are dropped by Witches upon death.
The above is the extent of what Kyubey tells the Puellae that make a contract with him. The following facts are not broadly known to most Puellae.
In fact, the Puella's soul is removed from the body at the time of her contract, and is housed within the Soul Gem. Becoming separated from one's Soul Gem by more than a few meters results in instant unconsciousness, and if the Soul Gem shatters the Puella dies.
Kyubey also tactfully omits the ultimate consequence when a Soul Gem becomes too unclean from overuse or emotional turmoil: the Puella becomes a Witch. Puellae are, in fact, the source of Witches themselves. This is done to harvest the energy released from the transition from Puella to Witch. Energy generated from the emotions of a human soul exceeds the amount of work required to create it, and Kyubey's species hopes to use this to combat entropy.
Kyubey typically selects young girls to become Puellae, because, according to him, they have the highest level of emotional fluctuation among humans.