Regarding the "races/factions"
First as said by Will, each race contains more than one "faction" because there are many independant or semi-independant duchy, principalities, chiefdoms etc for each race (the purpose in the tabletop game was that players could use their own schemes for painting).
The humans have several states and regional variations :
The Empire, is as said, the HRE from, mostly the XVIth century, with troops looking like landsknecht, knights in gothic plates, firearms, artillery etc. But also Orgres mercenaries, priests with powers, magicians and a few fantastic creatures like the Griphon of emperor Karl Franz. It is a major faction of the warhammer world (with a rulebook) and one, if not, the most powerfull human realm. It is divided in various principalities (with prince electors) and free cities. Playable.
Bretonia, is basically a feodal kingdom, imagine medieval France with some elements of the Arthurian cycle and an even greater segregation between the knightly class and the peasantry. It had become a major faction of the warhammer world with a rulebook so playable.
Kislev is some kind of medieval eastern state (with troops inspired both by Poland and Russia and also a few nomadic horsemen), it isn't a major faction and while there is (or was, i don't play the game) army lists, as far as i know they don't have a rulebook.
Tilea is separated into many rival city-states that often fight each others with mercenaries. They look like renaissance italy. They aren't a major faction either but mercenaries armies had an army list in the past (Dogs of War iirc).
Estalia is separated in small kingdoms, they look like renaissance (or pre-reconquista) Spain but aren't a major faction.
The borderlands is an area between Tilea, the Empire and the Wasteland (Orcish kingdoms and a few dwarf fortresses) full of small states warring each others and invaders, an area for adventurers and mercenaries. It is an area equivalent to the Balkan in the real world. Not a major faction, but a good setting for the old RPG.
Arabia is basicaly a version of arabia similar to the 1001 nights. Not a major faction.
Nippon is japan but only appeared as background for the world and with only brief mentions about ninjas and samourais.
Cathay is China but like Nippon, only appeared as a background element.
Halflings :
Basically the hobbits from the shire, they live peacefully inside the Empire and are one of the regions constituting this human state iirc the leader of the halflings is an elector too. Not a major faction, but the empire can hire some halflings as support.
Dwarfs :
Many dwarfs live in human cities and particularly inside the Empire. The Dwarfs and the Empire have a long lasting alliance dating back from the first emperor, the deified Sigmar.
The others live in independant fortresses in the various mountain ranges of the old world, a remnant of a old and mighty dwarven kingdom that was almost destroyed by the greenskins.
They are your typical fantasy dwarfs, tinkerers, miners, firearms, grudges, beer, beards, axes and hammers. Playable.
Elves :
There are 3 main elvish subfactions (each divided into various allegiances/principality/cities etc)
The high elves, who lives in Ulthuan (the atlantide like island in the middle)
Old civilisation, powerfull mages, powerfull stats... lol, seen as arrogant by others. They have varied troops, from basic spearmen and archers to knights, dragon knights, swordmasters etc. No firearms, but many kinds of advanced ballistas. Playable.
The wood elves, remnant of elvish colonisation of the old world before the humans came, they still live in the deepest forest. The major one being Lorien, close to Bretonia. They are hostile to strangers, but have some kind of understanding with the kingdom of Bretonia. Mainly light ambush and skirmish troops with their specialty "wardancers", light but deadly expert close combat troops. And also Ent, like in lord of the ring, walking treemen. Playable.
Dark elves, are a splinter from the high elves, rebels in a civil war, their claimant allied himself with chaos and many of its supporter fell to it too. They lost the war and exiled themselves i huge magically floating cities to Naggarod, the equivalent of north america. Basically evil raiders and slavers elves with cavalry on dinosaur, corsairs, assassins and deadly and scantily clad witches (close combat troops). Playable.
Undead :
Vampire counts. Well vampires who by being the nobility have managed to somehow seize the control of a whole imperial province near the borderlands, Sylvania (Transylvania). You have various kind of vampires (bloodlines), from the most classic ones to blood knights, they also can use various kind of classical undead troops. (Skeleton, ghouls etc). Playable.
Khemri tomb kings. Powerfull mummies who have been awakened with their armies of servants. (Classical undead troops with an egyptian touch). Playable.
Greenskins :
Orcs and Goblins.
They often fight together in a big Waaaagh (kind of a raid/crusade for greenskins) but can be separate armies or factions.
Several kind of goblins, night goblins live in deep cave and have exotic troops, squigs and squigs riders (you will have to google what is a squig i can't just explain it) giant spiders, untoxicated goblins flying huge iron balls etc.
"regular" goblins who are more some kind of ablative hitpoints for orcs than anything else although they have some kind of usefull and funny troops too. They can also field big creatures like trolls and Wiverns.
Then the orcs who are the muscles of the greenskins. Ferocious warriors if a bit simple... Playable, both of them.
Lizardmen :
As the name says, two main kinds, big shocktroops and small agile servants. A bit like the greenskins. They serves Slaan, powerfull magician and the oldest civilisation of the Warhammer world. The inspiration for their look is precolombian america (aztec/maya). They also field dinosaurs and the like. Playable.
Chaos :
The great ennemy of everything. There are "Chaos gates" on both poles of the wolrd, althought the one posing the main threat to most of the playable factions is the northern one.
There are 4 majors chaos gods with their own demons, champions and servants.
Tzeentch, the one seen in the trailer, god of change and magic, the great trickster, architect etc. Always planning the next move of his plans, so complex that even when you defeat him, you may have played how he had planned it.
Khorne, blood for the blood god ! The god of slaughtering and war. His champions and demons are among the most dangerous creatures of the Warhammer world.
Slaneesh, god of excessive pleasures, he is a young and decadent god with obviously a strong appeal for mortal followers.
Nurgle, the god of pestilence and everything related to illness and messy digusting things. His appeal lay mainly among the ones who are rejected and live in the margins of society, often victims of his pestilence themselves.
All of the followers of Chaos will end more or less mutated by its toxic nature at some points.
Chaos features several distincts kind or armies as well as featuring 4 main gods.
Beastmen, are man/animal hybrid born from the corruption of Chaos.
Demons, are well, demonic armies comprised of lesser and greater demons.
"Regular" chaotic warbands, made up of champions, cultists, demons etc.
And iirc, Marauding Norsemen who are some kind of evil vikings, think rather along the lines of naked and in fur madmen than along the line of your regular vikings (that would be the Norse).
Edit
I forgot the Skavens, who are mutated ratmen with a unique culture. They are a major threat to the old world, infest tunnels and sewers everywhere and are said to have a huge tunnel networks that allow them to travel where they want. The center of their power is located in marshes near Tilea (well, under said marshes...).
Poor infantry, ninja like troops, giant ogre/rat, wicked firearms using a corrupting stone, warpstone (think uranium ) and a few other exotic things.