In Magic: The Gathering's lore, the plane of Alara was split into five, and each shard lost two colors of mana. When all green and white mana is lost, Grixis is the result.
The Shards of Alara block explored multicolored themes in new ways, including five incomplete worlds and their unique ecologies. Bant is a world of sunlit kingdoms and ritual duels, and Esper is a world of metal, rock and sphinxes. Grixis, however, is a necromancer's paradise. It's a cruel world of undeath, twisted abominations and the desperate humans who try to survive in a world that is itself rotten.
The Dead World
Even the most hardened planeswalkers may be surprised and revolted by what they see when they visit this particular shard of Alara. Grixis is dominated by black mana, augmented with blue and red. There is no natural cycle of life or sense of civilization here, meaning it's everyone for themselves. The ground itself shows how vicious this plane can be. Any surface that isn't bare rock or murky seawater is made up of rotted flesh and piles of bones, as if the entire plane is a gigantic slab of corpses. Dead bodies are everywhere, either whole or in parts, and anyone who wanders around will be stepping on hills of diseased flesh or climbing up mounds of festering bones. It's like the plane itself is alive, and it's a zombie. Even the weather is in a bad mood; the sky is always shrouded with thick gray clouds, which often rumble with thunder and spit violet lightning. The stench of death is always strong on the wind.
As for its ecology, Grixis is a necromancer's version of the natural order. Life energy, nicknamed vis, is limited and is a prized resource among the necromancers and vampires who live here. For this reason, any living thing is hunted and ambushed to steal its vis, and necromancers often send their undead hordes for the job. Humanoid zombies are common, but so are zombified aven (called kathari), as well as bats and undead beasts of burden. Aside from the zombies, Grixis also features leviathans and krakens in its oceans as well as vast swarms of noxious insects from the Droning Isles. Ogres, called the incurables, wander the plane alive but tormented nonstop. Their twisted minds will attack anything they see, alive or not. If that weren't enough, packs of merciless devils roam the plane, eager to inflict suffering on anything they see.
All five shards of Alara have substantial human populations, and on Grixis, humans are on the defensive. They can't easily form kingdoms or carve out territory for themselves; the competition is too fierce. Instead, they retreat to fortresses, known as hermitages, using any creative magic they can think of to hold off the zombies and monsters who want to steal their life force. It's a classic zombie apocalypse scenario, plus magic and minus any hope of salvation and victory.
The humans contend with zombies, disease, a relative lack of food, swarms of flesh-eating insects and the constant threat of madness on this plane. Lethemancers are dark wizards who offer to drain away a client's memories to ease their suffering, a deal that may be quite appealing on a plane like this. The average Grixis human has seen and experienced plenty of things that they'd like to forget.
Grixis In The Game
In gameplay, Grixis has a strong graveyard theme. It introduced the Unearth mechanic, which only appears on creatures of Grixis colors. A creature with Unearth may enter the battlefield from its owner's graveyard when its Unearth cost is paid (only at sorcery speed), and that undead horror gains haste. It will be exiled at the end of turn or if it would leave the battlefield for any other reason, such as lethal combat damage or bounce effects. This ensures that an Unearth creature can only be revived once, but there are some ways around this. Sundial of the Infinite, a cheap artifact, can end the turn prematurely, which negates the "end of turn" exile trigger for an Unearthed creature. This is often done in the Sedris, the Traitor King Commander deck.
Otherwise, Grixis decks tend to be offense-oriented and can destroy the opponent in all sorts of ways. Red mana encourages quick attacks and burn spells, blue mana can shut down or bounce away blockers and black mana can destroy creatures and force the opponent to discard their hand. The ruthless, greedy nature of Grixis is best represented in its ultimatum card, Cruel Ultimatum. For UUBBBRR, the player will make an opponent lose five life points, discard three cards and sacrifice a creature. That alone generates massive card advantage, but the caster will also draw three cards, gain five life and return a creature card from their graveyard to their hand. In all the ways the opponent suffers, the caster of Cruel Ultimatum will revel in power.