I was listening to Episode 269 of Waypoint Radio and I heard that Patrick Klepek was trying to figure out the context for the events of Destiny 2 Shadowkeep. I thought that I would try and give a lighter explanation of what you would need to know in order to make sense of Destiny 2 Shadowkeep. Spoiler Warning for all the stuff in Destiny 1 and Destiny 2 basically.
The first thing to cover would be Eris Morn. Eris is a Hunter who lead a fireteam of four other Guardians (Guardians are the people who have Ghosts that can resurrect their partners) with Eriana-3, an Exo Warlock (Exos are the robots), to try and kill Crota, a Hive Prince (Hive Princes are extremely powerful Hive warriors). That fireteam failed to kill Crota and they all died save for Eris, who heard that sphere thing she carries around (which is a bone of Ahamkara, a shapeshifting species) tell her how to escape Crota, which she did, but she lost her eyes, so she replaced them with Hive eyes, hence the three eyes she has.
The red phantoms that you see around the Moon are the phantoms of dead species created by the Pyramid to haunt your Ghost and Eris Morn. The phantoms that hang around Eris throughout the campaign are the phantoms of her fireteam that died trying to kill Crota. The Pyramid decides to bring Nightmares, which are phantoms that can actually hurt you and possibly kill you, of old enemies from previous games and expansions to try and kill you. The boss Nightmares in the game that you encounter are Crota, Dominus Ghaul, Skolas, and Taniks.
Dominus Ghaul was the final boss in the Destiny 2 Red War campaign. Ghaul is a Cabal(the big beefy aliens with the big armor) who declared himself ruler of the Cabal Empire. The Cabal are warmongers and militaristic, kind of like the Roman Empire. The Cabal want to always be expanding their empire. Ghaul is the cabal who lead the attack on The Last City, the place where the Tower is located at, in the Red War campaign. You kill Ghaul and see him as a Nightmare in Destiny 2 Shadowkeep.
Skolas, Kell of Kells, was a Fallen Kell who tried to unite the Fallen in the House of Wolves expansion pack. The Fallen, known as Eliksni in their own language, are the insect looking species. They are raiders and scavengers who are trying to control the Traveler to regain their lost gifts that the Traveler gave them, hence the name Fallen. The Fallen people are divided by Houses, which are political bodies that act independently of each other. A Kell is a political leader of a Fallen House. Skolas was the Kell of the House of Wolves who was captured by the player in the House of Wolves expansion for betraying the Queen of the Reef, the leader of the Awoken (the blue humans) living in the Reef (a settlement living in the middle of an asteroid field).
Taniks, the Scarred is a Fallen mercenary who works for any of the Fallen Houses. The player meets him in The Shadow Thief strike, a strike in the House of Wolves expansion pack for Destiny 1. In the Shadow Thief strike, Taniks is hired by the House of Wolves to plunder the Hellmouth, a location on the Moon that you can go to in Destiny 2 Shadowkeep, but a fireteam of Guardians kills Taniks in the strike before he can send any treasure to the House of Wolves.
The Hive are an ancient race born from a pact with the Worm Gods. The worms come from the oceans of a far away planet named Fundament. The worms are disciples of The Darkness and draw their power from it, as do the Hive. The worms crave destruction and conquest, and since each Hive has a worm living in them the Hive need to fight or else the worm will consume their host. The Hive have a complex religious system based on complicated rituals and a pantheon of dark gods. The Hive religion is based on this idea called Sword Logic, which is basically Survival of the Fittest mixed with making sacrifices to their gods. Crota is a Hive Prince because he basically sacrificed a lot of Hive and killed a lot of things, which made him Ascendant. Being Ascendant means that a Hive got to the Ascendant Plane, which is a place related to the Darkness, and created a throne world in the Ascendant Plane where the Hive Prince rules over their own brood of Hive that are below the Prince. In the Dark Below expansion pack, Eris Morn asks you to destroy Crota’s army and eventually Crota himself in the raid that was in the Dark Below.
If you want to look up for more information about the things I covered in this post, I got my information from destinypedia. I know that I probably got things wrong in this so let me know what I got wrong and I will try to fix it. I hope this helps folks who want some context but don’t want to or don’t have the time to spend watching a nearly four hour video on youtube about the lore of Destiny.