The first episode to be aired on TV is entitled "The Finale", and it shows the huge and exciting climax to many storylines (as well as the final fate of all the characters). The viewer understands the general idea of the story (and it had better be a cool plot), but not the details. You know how sometimes you walk in on the end of something, and you don't really understand what's going on but it seems like something interesting enough to watch from the beginning? That's what this first episode is. And just for the sake of symmetry, the last episode of the entire series is entitled "The Pilot", setting everything up. So that feels like an epilogue, in the sense that it reinforces everything that the viewer already knows in a definitive sort of way. The rest of the show in between these two episodes is in a random order.
Each episode is an hour long, but the show is animated. (It's the only feasible way to pull this off, really.) Any episode, watched alone, is clear enough (and linear enough) in its storytelling that it can be a jumping-on point for the show. But the key to making the series work as a whole is that each episode feels like it's part of a big continuity. The characters are always dealing with the repercussions of events we don't know the specifics of, and many episodes feel like they've got to have major effects on what comes next. So an episode gets the viewer thinking about the bigger picture. The show is a big jigsaw puzzle which the viewer continues to assemble in his head from week to week.
But that's not why the viewer tunes in. He tunes in because every episode is a good story. You are surely familiar with half-hearted stories which exist mainly to get from point A to point B in serialized mediums. Those sorts of episodes exist in every show but this one. If point A is interesting, and point B is interesting, and the writers don't have anything particularly interesting planned in between, then point A and point B will each be episodes (Not necessarily in that order.) but the time in between will be skipped. Maybe somewhere down the line some writer will come up with some brilliant story which happens in between, so until that inspiration hits it's left blank. In general, that's how the show is written. There's no importance to the order the episodes are released in, except that that's the order the writers came up with the ideas in. An episode is only written if its writer really wants to tell that story. And it can take place at any point during the show's timeline- even before "The Pilot" or after "The Finale"! Further, an episode doesn't have an restrictions on how much time it covers. One episode might cover just a few pivotal minutes from many perspectives, and another might cover a single character's entire life! One writer could have a "pet" character which many of his stories focus on- the other writers back off of that character to some degree, to let him chart out the character's course.
No specific time frame is ever given for anything, so that the writers can say as many or as few stories as they like took place in a particular part of the timeline. So each episode written only creates more potential stories to be told, never less. In conventional shows, huge status quo changes are avoided because they prevent the writers from telling the stories they're used to. But here, the writers can always jump back to before the event. This encourages the writers to be more experimental with their plots.
There are many recurring characters, with new ones being introduced all the time. The premise of the show (whatever that is) lends itself to having some characters come and go all the time, on top of the core characters who are usually there. This allows tremendous flexibility in storytelling, not only because it doesn't lock the writers into using specific characters at whatever point in the timeline he's at, but also because it allows them to tell many stories not set in familiar locations.
The entire overall plotline of the show, in general terms subject to revision, is planned out before even the first episode is written. At the end of the day, the first episode needs to feel like it is the culmination of everything seen afterward. This keeps the writers somewhat focused, even as they tell their own little stories, because they always know exactly where they're heading in the long run. Not all the gaps need to be filled, of course. The viewer doesn't need to have it spelled out exactly what the context of "The Finale" is, because he's never going to get the entire picture. There will always be untold stories. But it should seem like the series is more than the sum of its parts. Writing the first episode is probably the hardest part.