When Desmond wakes up to start this episode, and is told by Widmore he's back on the island, he flips out. He yells about Penny and is told she's safe and sound and "the island is not done with" him yet.
What does this mean? Widmore's people force Desmond into a locked chamber, where they say they must conduct an experiment to see if he can survive another electromagnetic attack. They flip some switches and pull some levers and the experiment is on. Desmond screams to be let go as giant flashes of light hit him, he falls to the ground - and he's transported to the Sideways world.
This is his deal there: he works for Widmore, and is beloved by his boss. Like George Clooney in Michael Clayton, Desmond is a "fix-it" man. He makes lots of money and travels the world and has no family or connections of any kind. Widmore considers him a vital person in the company.
Visiting Los Angeles, Desmond is given a task by his employer: babysit a rock star that overdosed on a plane and is about to be released on bail: Charlie. Desmond, great company man, says he'll do it. Driven around by George (the freighter dude that died from the virus), Desmond meets Charlie. Right away, Charlie tells him about a near-death experience he had on Oceanic Flight 815, as he tried swallowing his bag of heroine in order to avoid arrest, and saw flashes of a women (he describes her as perfect and blonde... Claire?) and felt something he had never felt before: love.
Charlie says his goal is to get that feeling back. How? On the drive to the hotel (Charlie must be babysat because Widmore's son wants to play with Drive Shaft at a charity ball), he forces Desmond (who is driving by himself this time, no George) to drive into the water The car gets submerged. Desmond frees himself and swims around to try to help Charlie, who is just sitting with his eyes closed. As Desmond desperately attempts to open the car door, Charlie puts his hand on it and Desmond gets a flash/vision: it's of Charlie right before he dies on the island, with "Not Penny's Boat" scrawled on his hand. WTF?
Eventually, Desmond helps Charlie survive and they both end up at the hospital. When Charlie tries to flee, Desmond again confronts him, asks about Penny and is told about Charlie's flashes again and the idea of love. Charlie says Desmond should try and find Penny.
Without meaning to, this is exactly what happens.
Desmond is ordered to tell Mrs. Widmore than Drive Shaft can't play, and she receives the news (while setting up for her event) very well. And who is Mrs. Widmore? Eloise Hawking! She seems to recognize Desmond, and this is son verified, as he overhears the name "Penny" on the guest list and asks to see it. Mrs. Widmore pulls Desmond aside and scolds him. She says he has the life he always wanted, he's admired by her husband, he should stop searching for other things. Desmond has no clue what she's talking about.
When he goes to leave, the Widmore's son asks to speak with him: it's Daniel. He shows Desmond the drawings of a machine and many equations, which Daniel says he did late one night. But he's a musician, he had no clue what he had done. So he took his journal to a scientist friend, who confirmed it was the work of someone that had studied serious science his whole life. Daniel theorizes that he's blown up a nuclear bomb in the past and there's some other life, maybe, that they are all supposed to be living.
Oh, and Penny is his half-sister. He tells Desmons where to find her: running the stairs at a stadium. When Desmond awkwardly introduces himself to her there, they shake hands - and Desmond wakes up back on the island. Widmore says he was only out a few seconds, but Desmond has a new attitude. He's relaxed and happy. He's anxious to do whatever Widmore needs him for on the island. But just as he and Zoe are walking through the jungle, Sayid shows up. He kills a few of Zoe's co-workers and tells her to "run."
He then tells Desmond he can't explain, but they must leave. Still happy and chill, Desmond says okay. As he walks away with Sayid it, we're taken back to the Sideways world. Desmond is in the limo and asks George for a favor: get him the flight manifest for 815. He has something he needs to show everyone on there.