In my opinion, it's kinda like Lord of the Rings meets Conan and threw in dark fantasy to the cauldron...

The game begins with this old warrior telling a bit of the religion/mythology of the game and revealing some people pushed the Maker's patience by entering the Golden City (Basically DAO's version of Heaven). Because of this, the Maker (AKA, Dragon Age's God) cursed these people and the Golden City had become black, tainted by the intruders' hearts. Thus Darkspawn were born. They put a blight on the land which seemed unstoppable... Until the Grey Wardens showed up; warriors, rogues, mages, anyone worth a damn made the ranks of the Grey Wardens for one sole purpose: Kill darkspawn, end blights, save the world... Okay, so technically 3 sole purposes.
After this cinematic you create a character and see how they cross paths with this old badass of a warrior. Maybe you're the daughter of an Arl, who's castle was besieged and witness your family murdered. Or maybe you're an elf that's pushed around in a city's alienage and your soon to be wife is taken to a human lord's castle to be violated. Or maybe perhaps your a mage under the watchful eye of the Templars, most of which see you little different than the demons that huant and kill men. Point is, people push you around, you meet Duncan (That old warrior guy) who wants to recruit you as a Grey Warden and you leave your home to follow him into glorious (Or horrific?) battle...

"Awww crap... I should've stayed home to be pushed around..."
-Newcomer Grey Warden
Soooooooooooo yeah... It's a bit both glorious AND horrific... Especially seeing as though the king was betrayed by one of his most trusted and relied on of allies. To make matters worse, the betrayor blamed the Grey Wardens for the death of the king while a blight is on and now has taken power. His great leadership plan? Preventing a neighboring country from invading and raging war despite no sign of such hostility from that nation and ignoring the grotesge monsters sweeping the land like a vile plague... Yeah, great idea King Bonehead...

Is everyone so incompetent that I have to solve their problems? Really, can't someone else overythrow the spaz dictator? ... No?!?! Fine, add it to my To-Do list..."
-Newcomer Grey Warden
Yep, the game has too major threats: Darkspawn horde led by a monster of a Dragon known as the Archdemon, to a paranoid and calculating tactician of a douchebag that wrongfully (And poorly) sits on the throne and leads armies. So now you gotta travel the lands, do errands for everyone, form an army of your own, kick the ass off the throne, decide to kill him or have him join your Grey Warden ranks (It's a totally political BS reason), then go kill the archdemon and end the blight... There is a cost for that but SOMEONE tells you can avoid such a heavy burden if SOMETHING gets done... Won't lie, sex is involved.

"... Wait... What?! ... I'm not gonna like this, am I? ... Who wrote this story? Mad Wolf?!?! Maker, I hate that guy..."
-Alistair
Not a joke, sex IS in this game and although they wear underwear (Why I don't know, the Dragon Age series has topless monsters, some super gross to look at, so bras in the sex scenes just seem... Kinda dumb) the scenes are fun but are done tastefully and seem romantically tender so no, nothing really pornographic or nothing, sorry to all the perverts.
The game is pretty epic... Epic story, epic battles, freakin' great music, badass amount of blood and gore getting showered on your face/armor, gameplay gets more than challenging, amazing character backgrounds (I particularly love Morrigan, the cold hearted Witch (shrew) of the Wilds...

"Charmed... Really, I am..."
-Morrigan
I also love a DLC character named Shale, he's a Golem with free-will (Unlike other rock monsters who act more like stone robots with no personalities) and a fear for being pooped on...

"Watch the skies, Dragonborn... Forget dragons, those damn pidgeons can swoop down anytime."
-Shale
I give Dragon Age: Origins 5 out of 5 vials of Darkspawn blood... As though it needed more...