A Sigil (シギル) is an ability all players taking part in the Darwin's Game possess, granted once they join the game.
Not much is known about sigils other than they are otherworldly superhuman abilities granted to players of the Darwin's Game with each and every player who takes part in the game receiving a randomized and unique sigil immediately upon creating an account. Players automatically know how to use their sigil (the only known exception to this being Kaname) and it's impossible to change your sigil once gained. Executives of the Kuchinawakai are all said to have the same sigil.
In the extra chapter of volume 7, Kashiwagi Rein states there four ranks to sigils and lists their percentages along with her own reasoning on the naming rules: 75% are "Animal Rank" sigils that have an animal's name, either transforming the user's body or expanding their five senses; less than 20% are "Superhuman Rank" sigils whose names are based on the function of the sigil, many of these are unique; less than 4% are "King Rank" sigils that have the kanji of royalty in them and are mostly powerful telekinetic types; and finally, less than 1% are the extremely rare "Myth Class" sigils that are named after gods.
People from Japan in World Line O refer to sigils as Koujinryoku (荒神力) and only officers of the imperial guard have been shown to use it so far. It's also been stated that the imperial family is apparently monopolizing the koujinryoku and there are those that don't like it as they believe sharing it to everyone would result in equality. Those people are later revealed to be agents of the Great Russian Republic who refer to sigils as Exen (エクセン).
Telekinetic (念動系) type sigils give the user the power to manipulate specific materials or items, which range from the user's own body, other people, or simple inanimate objects. Examples of this type include Karino Shuka's Queen of Thorn and Wang's Beelzebub.
Metamorphic (身体変化系) type sigils can either completely or partially change the user's body into a totally different quality or shape from their original form. Examples of this type include Danjou's Wall Iron and Hiiragi Suzune's Mag Mell.
Mind Control (精神操作系) type sigils are capable of directly influencing the mind of a target; imposing thoughts, actions, and/or demands upon the subject, though some only work on humans and specific animals. Examples of this type include Ayanokouji Kaito's Peace Maker and Themis' Unbalance.
Sense Expansion (感覚拡張系) type sigils either strengthens the user's five senses or bestows them with a unique form of sixth sense and because of this they're also referred to as "ESP types". Examples of this type include Maesaka Ryuuji's True or Lie and Kashiwagi Rein's Laplace.