Leslie Knope had the brilliant idea to put a time capsule in the ground that was filled with things that represent the town of Pawnee. In true Pawnee fashion, the town's ideas were all over the place.
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Enter Twilight. Will Forte (hey buddy!) guest-stars as a father who's adamant that the Twilight series be included in the capsule. So adamant, in fact, that he handcuffs himself to a chair in Leslie and Tom's office and stays there for days. Tom Haverford has just recently been dumped by his girlfriend Lucy. She broke up with him because he's been too obsessed with the fact that Ron Swanson is dating his ex-wife Karen and Tom is quite depressed about it. Lucy even pops up in the episode to tell him that if he ever gets over it, she'd be willing to give it another try. Tom is too thick (or now, too Twilight-obsessed) to truly understand, and he's left alone with his tween vampire books.
Also in the episode, Andy and Chris bond because Chris believe "Andy is a good guy." So, they begin to devise a plan to win April back—but it doesn't really move past the brainstorming session because they only positive dating factors Andy could come up were "nice" and "in a band." Lucky for him, though, April's new flame (a Dave Matthews Band fan) also comes around to Andy after listening to Mouse Rat's album. Advantage: Andy.