In which we meet the Cast, possibly get a hint of things to come, maybe introduce the Big Bad, and most importantly show what the series does.
It's probably largely a Monster Of The Week episode, so see below for talk about those. It differs from a regular MOTW because it shows the Cast coming together to fight some threat and save the day, re-establishing the group dynamic, and also proves the power of the Chosen One, which has to be demonstrated generally by being questioned.
"I'm Buffy. The Vampire Slayer. And you are?"
The first of these is the Series Pilot, where you have to lay out pretty much everything audiences can expect, the basic rules of the setting and all, while also telling a story that makes them think they'd like to see another one next week. Hopefully your players are relatively keen to begin with, but you still have to hook them good.
But every one has to be a good jumping-on point for new arrivals. So if your show is called Buffy The Vampire Slayer then Buffy should slay some vampires. You can get away with her slaying other kinds of monsters every third Season Opener, as long as there are special circumstances like abandoning her mission or coming back from the dead. (In the latter case, I suspect new viewers on the new network would still have been very confused, but never mind.)
It should give all the player characters in the cast (and any major NPCs, such as a handy exposition Watcher) a moment in the spotlight as well as establishing the Hero's badass credentials.
If it isn't the pilot, then there may be changes in the status quo to deal with.
New player characters (possibly with new players attached) are the most important. How are they introduced? The Watch House had the subtle-as-a-brick tactic that new PCs would, by default, be of interest to the Watchers and would therefore be introduced to the Cast at the start of the academic year / season. More character-specific methods can be woven in with a bit more warning. And you can say "you always had a little sister" but that's really a one-time trick.
Other changes can be logical fallout from the previous seasons, new developments (which may or may not make any sense to begin with), new NPCs arriving much like new PCs and so on.
If the Cast killed the ancient vampire who ran the town in secret for centuries, this creates a power vacuum that a new Big Bad could fill. If the whole town fell into anarchy when Pandora's Box was opened, the new season can start with it being declared safe to return to, you bet. If one of the PCs was thrown into Narnia and the player wants to play them again, you'll need to dress for cold weather.
And in amongst all this, you also have a MOTW. It can be simpler than average, but also bigger - see above re hooking the audience. A big gang of vampires planning some evil ritual is fine, you can get away with that two years in a row in fact.
Pilot Example: Number One Hit
Will Play For Food forms at Totally Not A Hellmouth U, Billie the hella-fast drummer being one of the potential members to try out. But little do the rest of the band know that she has a dangerous secret and she keeps those drumsticks with her everywhere she goes for a reason...
And meanwhile, drawn to the blood of the slayer, an ancient evil stirs...
Opener Example: One Two Three Go
After Billie and the band defeated Crossroad, lead singer Hope has been robbed of her talent and the group has split up. What would it take to bring them back together?