A more accurate summary:
* The Imperium of Man and its subfactions: Scary Dogmatic Humans. Xenocidal and imperialist, as happy to wipe out billions of its own people as it is to exterminate entire alien races.
* Chaos: Extra-dimensional malevolent gods and daemons that are capable of crossing into the physical realm and corrupting the minds and bodies of sentient species. Four principal Chaos Gods and countless lesser deities and daemon princes, served by billions of cultists and thousands of ancient daemon-corrupted Super Soldiers who rebelled against the Imperium during a galaxy-splitting civil war ten thousand years before the setting. Unquestionably evil, delighting in murder and depravity. The four main gods are born from the emotions of hope, love, bravery and acceptance; this should tell you most of what you need to know about 40k's place on the Sliding Scale Of Idealism Versus Cynicism.
* Eldar: Elder Race with massive superiority complex. Through their past depravity responsible for creating the Eye of Terror. Not quite Xenocidal, but consider the deaths of millions of humans to safeguard a few hundred Eldar lives more than a fair trade, and have the psychic future-prediction and manipulative skills to make that sort of thing a reality rather than a dream. As an example, they tricked the Ork warlord Ghazghkull Thraka into attacking the human planet of Armageddon, setting off the Second and Third War for Armageddon, killing billions of humans, just to prevent Ghazghkull from attacking one of their world-ships.
o Dark Eldar: Offshoot of the Eldar that still practice the same depravity that led to their race's fall. Sadistic in the extreme, need to feed on others' souls to avoid their own being devoured by the Chaos God Slaanesh.
o Exodite Eldar: Descendents of Eldar who left before the fall to live simpler lives on planets with harsh conditions. Their tech is deliberately less advanced than that of their Craftworld counterparts, and by choice they are reclusive, sticking to their own planets for the most part, making them Wood Elves in Space. They are a background plot element rather than a playable faction, but unofficial army lists have been made for them, complete with dinosaur-riding, laser-lance-equipped knights.
* Orks: Genetically engineered by a precursor species as a biological weapon. Peculiar biology (see Plant Aliens), personalities based on ridiculously exaggerated football hooligan stereotypes, all "boyz" and speak with Funetik Aksents. Violently sociopathic, prone to infighting, and genocidal, but all in good fun; an Ork "Waaagh" is described as a combination of mass migration, pub crawl and holy war. Highly psychic, but not aware of it - Ork technology only works because the Orks THINK it should. This also has other effects - for example, Orks piously believe "da red wunz go fasta", so if an Ork paints his bike red, it will go faster.
o An entire spinoff game, Gorkamorka, concerns a planet full of Orks that holds no strategic importance to the other races, with the Orks having no way off (having turned their space hulk into massive statues of two gods... and then destroyed them). They pass their time with a massive, futile tribal war between themselves.
* Tau: Technologically advanced humanoids with a rigidly caste-based society. The Ethereal caste rule over the Earth, Air, Fire and Water castes, who are all utterly loyal and devoted (one theory has it the control is based on pheromones). They see themselves as benevolent imperialists fighting religiously for the 'Greater Good,' and are singled out for being the only faction that seriously engages in diplomacy or offers anything other than genocidal total war. Despite a thing for mass sterilisation, warmongering and concentration camps, they really are the nicest people you'll find in this galaxy. Imperialist, expansionist, slightly fanatical ("slightly" in this setting meaning that only one mech per army can be upgraded to a suicide bomber.)
* Tyranids: Extra-galactic locusts in apparently limitless numbers. If they take over a planet, they devour all organic material, eat the soil, drain the geothermal heat from the planet's core, drink the oceans and suck up the atmosphere, leaving an airless rock. Hungry. Extremely psychic, with the psychic chatter that forms their Hive Mind being so powerful that their mere presence drives psychics insane and interferes with technology that uses psychics - including interstellar travel and communications. Bug Wars crop up wherever they go, with the suggestion that the three galaxy-eatingly-enormous, near-unstoppable Hive Fleets are just scouts for the real invasion.
* Necrons: Ancient undead metal constructs powered by the souls of long-dead aliens that hate all living things. In thrall to gods that wish to consume all life. Ridiculously advanced technology, almost impossible to kill, omnicidal down to the last bacterium.
