A lot of D1 will be briefly explained throughout the game, I would assume. But, in brief:

PREWARNING: I MAY BE WRONG ON SOME THINGS

We destroyed the 'black heart' which was calling for more darkness (enemies) across the galaxy (I think - nobody knows).

An enemy, necro-looking race called the Hive had a God called Oryx - so we killed his son because he was sending his Hive everywhere to take over

We helped the Queen of the Reef (A place where some humans went to escape but they got radiation poisoning basically and turned into people who glow) with some Fallen enemy who betrayed her people.

Oryx, the Hive God found out we killed his son and got pissed, so he transformed all of the enemy races, Vex (Machine), Fallen (Like humans but with more arms and legs), Hive (The necro lookin' dudes) and Cabal (Angry, fat military things) into 'Taken' - basically reskinned to look black and cool but with super powers. To take him down the Queen of the Reef 'dies' (Maybe not, hopefully) helping us breach his ship, boarding and killing him - Team Rocket style, flying off again (into space).

This old team of Guardians called the Iron Lords trapped away a science project called 'SIVA' which could basically make anything. When we walked ourselves off into the last city of Earth, the Fallen found the SIVA and used it to enhance themselves. We blew them up

D2. The Cabal's Red Legion have come to take the Light (The Traveller's powers given to us from the big orb in the sky) because they believe it was meant for them (because it moves from planet to planet). So they cage it which takes away our powers. The last city of Earth is blow the fuck up leaving us with no home and no powers

I think that's it in brief. There's literally tonnes more info out there on things not even in the game. Check out a video on the history, but don't worry too much since it'll be covered in the sequel! Have fun!