When they try to investigate the meaning behind this monster mash, they're ambushed and thrown into a creepy underground dungeon with no way out.
That's when Paula uses her telepathy to contact the only person who can help.
Jeff is awakened from his sleep by the psychic call from across the ocean. Much like Ness and the meteorite, Jeff's call to action comes in the middle of the night, interrupting what should be a regular night in his regular life at the Snow Wood Boarding School in Winters, a perpetually snowy town in Foggyland - a clear representation of the UK.
He gets up, totally dressed in his school uniform, and heads for the door, when he's halted by his friend and roommate Tony, who comes with him.
Everyone else at the boarding school is still awake, gathered in a common area, talking. It seems like Jeff and Tony are those kids. Introverted. High maintenance. On the spectrum?
Seemingly the only teacher at Snow Wood, Maxwell, provides Jeff with a machine to open the lockers in the locker room so he can gather equipment. Indeed, the machine can open any lock. Man! Presumably, Maxwell can trust a good kid like Jeff with this sort of thing.
Tony, without asking why Jeff has to leave, helps his friend scale the gate of Snow Wood.
I don't know where you're going or why...But remember, we are best friends forever.
A lot of people have made fun of Tony, with his dopey hat and his perpetual O face. His relationship with Jeff doesn't quite read as a bromance, so people assume that he's gay. And, since the game's release, it turns out that he is! According to Itoi, in so many words.
So it's true. It seems that Tony loves Jeff, whether or not he knows it. And Jeff is leaving behind the one person who loves him to go somewhere he doesn't know to do something he's not sure of.
As Jeff journeys south, he passes a drug store that sells weaponry for Ness and Paula. There's a shortcut that is blocked by an iron pencil statue. There's a glowing light in a cave that says, Only Ness can absorb the power of this place. Even so close to home, so much is around to remind him of his destiny intertwining with Ness'. And telling the player, "Look forward to coming back to this place!"
Finally, you make it to the southern laboratory, and finally meet Jeff's estranged father, Doctor Andonuts, who doesn't even recognize him at first.
Uh, those glasses look good on you. How about a donut?
>Yes
No
Well, I was only offering... I'd also like a donut right about now.
He lets on that he, too, had been contacted by Paula for the purpose of getting Jeff to Threed. He mentions his Phase Distorter which is incomplete (remember that!!!!!!), but ultimately offers his Sky Runner.
What do you think? Isn't it neat? Get in! Let's get together again in 10 years or so.
Jeff boards, and it automatically takes him to Threed, flying over a few locations that Ness and friends will visit in the future - revealing the locations of treasure in a certain desert.
Jeff's role, aside from being the guy who uses bottle rockets and wins boss fights, is being the loner. He doesn't come from a loving family like Ness and Paula. His father never visits, even though he's not far away. The only encouragement he gets is from a teacher (Maxwell, not the Doctor, saves his game data). He only has one friend, and the both of them are kind of losers. The bubble monkey, who accompanies him south from the drug store, abandons him to pursue the love of a lady monkey.
Ness is a good kid, and most definitely a swell avatar for the player. But the truth is, most kids who play and love Earthbound are probably more like Jeff. Reclusive and unpopular, not especially talented in most things, but deep down quite proud and real fucking smart.
We have seen the family lives of Ness, Paula, Pokey, and now Jeff. The most important lessons that Jeff teaches are that suffering an awkward adolescence will provide you with the self-knowledge to become a better and more dependable person in the long run,
and that your family, big or small, are the people who love you.
EDIT 12/19/14: This sums it up nice.