The opening episode is a gigantic Royal Rumble of characters duking it out, which ends with Skeletor tricking He-Man into stabbing him in the chest. This somehow lets him get his hands on the Sword of Power and gets control (or starts to get control) over Castle Grayskull. He-Man splits the Sword of Power to stop him, but doing that explodes both him and (apparently) Skeletor. He turns briefly into Adam while doing it and this is how Teela finds out they're the same person.
Time skip and everyone's sad. Teela ragequits because she feels betrayed and also sad over Adam. Sorceress is dying, magic is dying, and Eternia is dying. We find out Eternia is actually the lifeline of the universe. If it goes, so does everything else.
They have to find the two halves of the Sword of Power. This means going to Eternia Hell (Underworld) and Eternia Heaven (Preternia). Man at Arms can reforge the Sword of Power, but he's stuck in Grayskull as the Sorceress' only defense against the fragmented Evil Warriors. So they send Roboto with Teela because Roboto can theoretically do it too. Maybe.
Teela gets her maybe-girlfriend, Orko, Roboto, and Evil-Lyn as her Fellowship of the Ring. They go to the Underworld where Scare-Glow is guarding the evil half of the Sword of Power, and there's also a portal to Preternia. (Huh?)
Big fight happens. Scare-Glow feeds off fear, and Teela's afraid she isn't good enough, so the fight spills over into Preternia.
Orko dies in Episode 4 in a heroic sacrifice against Scare-Glow. Apparently this feels pretty "final" as deaths go. They make a grave for him in Preternia.
They find Adam hanging out in paradise with the rest of his He-Man ancestors and explain what's going on. (Moss Man is also dead and in Heaven. I don't know why.)
There is a portal back to Grayskull from Preternia (there's a portal just about anywhere in this show, apparently), but whoever goes through it can never return (isn't this
All Dogs Go to Heaven?). Adam voluntarily gives up any chance to return to Preternia in order to return to Grayskull with his friends.
Roboto reforges the Sword of Power, but dies in the process. I guess this thing is a radioactive hazard or something.
Once they're in Grayskull, there's another big fight between Man at Arms and a few Evil Warriors where he basically solos them. Teela, Adam, and the group get down to the inner depths of Grayskull where Adam raises the Sword of Power to turn into He-Man...
...and Skeletor pops out of Evil-Lyn's staff, where he's actually been hiding the whole time. He stabs Adam right through the chest, possibly killing him (?). He takes the Sword of Power, holds it up, and does the famous chant: