Cleric Domain
Cleric Domains, commonly abbreviated to Domains, are a mechanic from Dungeons & Dragons that serves to provide greater individuality for clerics.
Much like how wizard magic is divided into its eight schools, one would presume that the powers granted by the goddess of earth and healing would be different to those granted by the god of fire and plague. Domains, then, serve as a way to mechanically differentiate clerics based on their patron gods, and can even be used to define adherents to specific sub-beliefs or sects of a particular god.
The concept of the Domain has been around since at least the days of Advanced Dungeons & Dragons, and isn't going anywhere any time soon.
AD&D
The foundations of the Cleric Domain were laid in two AD&D mechanics; Spheres and Specialty Priests.
Spheres were direct priestly correlations to the wizardly schools of magic; they represented divine portfolios, areas of influence that a god would have dominion over, and so they had magical spells based on that portfolio. Depending on what god you worshipped, your cleric had access to certain spheres, which informed the kind of spells you could cast - Sun spells, Nature spells, War spells, etc.
Specialty Priests were a form of priestly kits that were used to represent specialized followers of specific gods. This gave the priest different mechanical edges and disadvantages, depending on what kit was chosen.
3rd edition
The iconic form of the Cleric Domain, if only due to its lifespan, was made in 3rd edition. This version of a Domain granted a cleric access to both a small list of bonus spells that would not normally be on the Cleric spell list and a single passive mechanical edge - for example, an elemental domain would usually grant the ability to turn and rebuke elementals of the "enemy" element as if they were undead.
In this edition, clerics select two Domains at 1st level, representing the particular divine portfolios that their faith resonates with.
4th edition
In something of a throwback to AD&D, 4th edition Divine classes - the Cleric, the Paladin, the Avenger, and the Invoker - didn't initially have Domains. The idea was that the sheer variety of powers, feat-based "worshipper of X" class bonuses, and paragon paths could grant quite a bit of variety to a clerical concept as it was.
But, Domains were too potentially interesting an idea to just up and abandon. So, the "Divine Power" splatbook contained a whole segment dedicated to reintroducing Domains. In addition to examining them from a fluffy angle, and how to respin Domains for odd-seeming alignment fits - a Good God of Destruction, a Chaotic Evil God of Freedom, an Evil God of Protection, etc - it provided mechanical details for making them work.
4e Cleric Domains take advantage of the comparatively high number of feats that a 4e PC gets access to. Each Domain has two associated feats; one that grants a permanent passive bluff and takes on a special rider to a thematically approriate set of at-will powers, and one that provides a new, thematic way to use the Channel Divinity class feature.
5th edition
With 5th edition taking the approach of mandatory subclasses, turning Domains in the cleric subclasses was as natural as turning the schools of magic into the wizard subclasses. As in 3rd edition, a 5e Cleric Domain grants a list of bonus spells for all of the spell levels. More importantly, it also grants a number of bonus class features, at levels 1, 2, 6, 8 and 17, which mechanically alter how the cleric plays and what it can do to a far greater extent than the oft-meager domain powers of 3e.