Well now I'm curious to know more.
How much time do you have?
The current season is called Season of Arrivals. Bad guys are arriving in the system and doing terrible things.
The Traveller, the big white ball in the sky over the tower, is currently chilling out and not doing much. It seems like it's in recovery mode after getting chunks ripped out of it at the end of the Red War (the original Destiny 2 campaign where Guardians lost their light, Dominus Ghaul and the Cabal showed up and wrecked shop before being turfed out by the player and their buddies). Trouble is, we could really use it doing something.
At the end of Shadowkeep (the most recent expansion) we found an artifact in a pyramid ship that had crashed on the moon a long time ago before being covered up by the Hive. The artifact started to pulse with Spooky Energy which led the players to The Black Garden, a place that's been hinted at in the lore for a good long time. While there this happened and we discovered that oh no the pyramid ships belong to the Darkness. They're pyramids, and they are working with the Hive and the Taken and other enemies.
The season before last had a character called Rasputin (an ancient warmind AI built during the golden age before the collapse who was on Mars and controlled a system wide defence network) had us completing public events to launch satellites to re-establish his defence grid. Everyone's very, very cautious about Rasputin because in the past he's done some pretty inscrutable stuff that's caused a lot of people to die. He's only recently started to talk to us and he seems good, but at the same time, the entire Cosmodrome is off limits because of a thing he did. Giving him access to a huge amount of guns might not have been the best idea anyone's ever had.
Doesn't matter, though, because at the start of this season, he pointed all those guns at a Pyramid ship as it entered range, fired them and the ship just kind of paracausal'd its way out of the shot. Rasputin, having fought the Darkness before in the Golden Age, then had a PTSD meltdown and went offline in a panic.
Since then we've been moving to evacuate planets to Earth. We've also been using technology created by The Driferter (Dredgen Camille Yor to use his full name and title) to draw The Darkness towards it, fight Taken and gather motes of darkness (you know those orbs of light that get created when you use your super? Like those but in reverse), stuff them in a container and process them into Umbral Essence which can be then used by a three-eyed goth wizard lady who's haunted by seven ghosts who's found a silver tree growing on Io, site of the Travellers initial landing in the system.
Like, that's the basics of what's happening this season.