Stories in multiplayer.

I think that what they were trying to say was that the thematic challenges every week will form a story line of conquest or some such, or will be connected to some sort of an out-of-the-game fiction one of their staff will pen down. Just like they had some fictions penned for SWTOR on their website.

Conquest in SWTOR had sort of a Theme set up for every week with a selection of activities that fall under the fold of that story.

I doubt that the MP zones themselves will become more like story-telling MP challenges like the story-driven repeatable flashpoints and Operations in SWTOR. Those were extremely hard for them to produce en masse.

They already swore up and down that nothing you do in the MP will impact the narration in the game (unlike the infamous ME3 endings).

I am all for a narrative outside the game that allows you to insert your favorite MP characters and pick up the Weekly "dossier" or "orders", depending on your level of character promotions (I suppose) from the central hub like the N7 HQ was. It could be that you'll get a weekly terminal of those tasks in the game itself, like the Weeklies in SWTOR on the Fleet.

if the single player weirdos try the mp they will like it, BUT they must try it lots of times, they will be in the floor waiting for the waves to be over for the first 50 - 100 games,
then, they will love it

and i hope there is some depth/context to the MP, some connection with the main story

BIG MISTAKE! RAAAAHHH!