Splat is a generic term for factions or groups in White Wolf games, e.g. clans, tribes, factions and kiths. A more official term sometimes used, especially for games in the Chronicles of Darkness, is "character axis".
History and origin
Back in the days of early dot-matrix printers, the asterisk resembled a squished insect, with six legs splayed out. As a result, it was often referred to as a "splat" by programmers who wished to save time (something like calling the "exclamation point" a "bang"). In later computer usage, it was often used as a wildcard character in searches to represent any or all results; e.g. searching a directory for "*.bat" would display all files that ended with the .bat extension.
As a result, on USENET when discussing the clanbooks (and tribebooks, tradition-books, etc.), many people began referring to them as "*books." This evolved into the term "splatbook." Naturally, it followed that a clan, tribe or other faction would therefore be a splat.
Splat axis
Each new World of Darkness game has two "axes" of (usually) five splats: one inherent and supernatural, and one chosen by the character, which may be social, political or philosophical. (There is often a sixth choice representing no alignment on this second axis, with several additional splats presented as options for Storyteller characters.) This arrangement is generally referred to as the "5x5" system. Each game also has an additional minor splat type (like Kindred bloodlines) that are unavailable at character creation, but may be joined later; examples of these are presented in each core book, with more presented in later supplements.
Some earlier games used similar inherent/social divisions of splats, notably Werewolf: The Apocalypse, Wraith: The Oblivion, Demon: The Fallen, and the Dark Ages: Vampire revision of the Dark Medieval setting.
Fatsplats, secondary splats, and tiers
Exalted has much larger hardcover supplements, nicknamed "fatsplats", which tend to cover an entire type of Exalted (such as the Lunars or Alchemicals). This term was later applied to the various Chronicles of Darkness game lines (Vampire: The Requiem, Werewolf: The Forsaken, Mage: The Awakening et al), which are all arguably fatsplats of the main CofD: World of Darkness: Storytelling System Rulebook 
.
In many games, some splats have minor or secondary splats that function as a subtype of a particular parent splat. The most prominent examples of these secondary splats (or "sub-splats") are bloodlines, which are a subset of the clans in both Vampire: The Masquerade and Vampire: The Requiem. Likewise, several games feature factions as a subsplat of a social splat.
Hunter: The Vigil introduced the concept of organizing splats by tiers of influence. Tier 1 "splats" are small-scale, and exist only on the equivalent level of the player characters' troupe. Tier 2 splats function on a city- or region-wide level, while tier 3 splats are global in scope. Danse Macabre introduced the concept of tiers to Vampire: The Requiem, establishing the extant social splats (the covenants) as existing at tier 2. Imperial Mysteries introduced the notion of tier 4 splats in Mage: The Awakening; these splats function on a cosmic level of play.
Splat types
Ars Magica
Ars Magica introduced the concept of splats, although the term did not emerge until after the game had left White Wolf's hands. The splats in Ars Magica are the Houses of the Order of Hermes, some of which would be retained when the Order was reinvented by Mage: The Ascension.
Classic World of Darkness
While multiple splat types existed in Classic World of Darkness games, the majority had only one main type. These "main splat types" are bold in the following entries.
- Clans (and bloodlines) and sects in Vampire: The Masquerade.
- Dharmas in Kindred of the East.
- Roads (in addition to clans and bloodlines) and Paths in Vampire: The Dark Ages and Dark Ages: Vampire.
- Legacies in VTM: Kindred of the Ebony Kingdom
- Breeds, auspices and tribes in Werewolf: The Apocalypse.
- Traditions, Conventions and Crafts in Mage: The Ascension. The Traditions have the sub-splats of Factions (or Houses in the case of the Order of Hermes); their counterparts within the Conventions are the Methodologies.
- Guilds and Legions in Wraith: The Oblivion. Membership in the Hierarchy, Heretics or Renegades can also be considered a social splat.
- Kiths, Houses and Courts in Changeling: The Dreaming.
- Creeds in Hunter: The Reckoning.
- Amenti (Tem-akh) and Factions in Mummy: The Resurrection.
- Houses (the Sebettu) and Factions in Demon: The Fallen.
- Orders in Dark Ages: Inquisitor.
Trinity Universe games
It is notable that Aberrant is perhaps the only major White Wolf game that does not have splats; every Nova is considered unique. The closest characters in Aberrant have to a splat is their allegiance, which has no mechanical bearing on the character and which may change organically over the course of play.
- Psi Orders (and corresponding Aptitudes) in Trinity.
- Inspiration type (Stalwart, Daredevil or Mesmerist) in Adventure!.
Exalted
- Castes for Solar, Lunar, Sidereal, Abyssal, Alchemical and Infernal Exalts (though each has their own unique set).
- Aspects for Terrestrial Exalts.
Chronicles of Darkness
Most Chronicles of Darkness ("New" World of Darkness) games use the "5x5" axis system, as described above. In this list, the inherent splat is given first, and the social splat is second. Minor splats and exceptions are described after these two main axes.
- Clans and Covenants in Vampire: The Requiem. Bloodlines, offshoots of the clans, may be joined after character creation. The covenants have a number of minor factions, though these rarely come into play.
- Auspices and Tribes in Werewolf: The Forsaken. Lodges, a social minor splat, are usually joined after character creation.
- Paths and Orders in Mage: The Awakening. Legacies may be joined after character creation; some are tied to specific Paths. The orders also have a number of minor factions.
- Lineages and Refinements in Promethean: The Created. While there is no true minor splat, Athanors serve a similar niche and may only be created during play; each is associated with a specific Lineage.
- Seemings and Courts in Changeling: The Lost. Changeling breaks with the 5x5 model, with six Seemings and only four Courts. Seemings have sub-splats called Kiths which are optional but must be chosen at character creation. Entitlements may usually only be joined after character creation; some are restricted to members of certain Courts.
- Compacts or Conspiracies in Hunter: The Vigil. Unlike the other World of Darkness games, Hunter only has the one splat type; compacts are simply a lower-tier equivalent to the more powerful and influential conspiracies. Some of the conspiracies have factions (or divisions, in the case of Task Force: VALKYRIE).
- Thresholds and Archetypes in Geist: The Sin-Eaters. Archetypes (of which there are eight) are a more minor part of the character mechanically, functioning more like Virtue and Vice than other splats. Of more immediate consequece are the Keys chosen by the Bound which determines what powers they have access to, although Keys are somewhat dependent on Threshold.
- Decrees and Guilds in Mummy: The Curse. Both decree and guild have an effect on what affinities and utterances a mummy has access to, as well as the strength of their pillars.
- Agendas and Incarnations in Demon: The Descent.
- Families and Hungers in Beast: The Primordial.
Scion
The "splats" used in Scion are the scion's parent god, and the pantheon to which that divine parent belongs.