So there's a rather notorious condom featured throughout The Story of Us. Josh keeps it in his wallet—you know, just in case—but he stole it from him brother so long ago that it's kind of old. Kellan and Emma joke about it: "Why do guys carry ratty old condoms in their wallets? When they finally get around to using them, they're either expired or worn out" (38.42). Which is most certainly true when it comes to the one Josh carries.
The condom represents the fascination that all the characters have with sex. It's on the brain big time, but at the same time, the condom isn't ever used. And although these characters have thought about it, none of them have yet made the decision to have sex. So in a way, the condom actually symbolizes their innocence, as well as their age. They're teens, so sex is on their minds, but none of them have taken the, er, plunge yet.
The condom also comes to the rescue when Emma's trying to keep Kellan from getting pregnant. She remembers that Josh has it in his wallet and manages to sneak it into a jacket that Kellan borrows. Given the joke she makes earlier about guys and old condoms, though, we're not really sure why she thinks Josh's will do what she hopes. But perhaps this is just another example of how the condom, instead of representing promiscuity or something like that, really represents innocence.