Yeah, the Elite Four. The four strongest trainers in the league. Like the gym leaders, they all specialize in a specific type. You can only challenge them after you have all eight badges. Though it might be all sixteen here, because of the two regions. Or at least under normal circumstances, since like I said, they don't seem to be accepting challenges right now.

Anyway, if you manage to defeat all of them then you get the chance to take on the Champion, who is basically the big kahuna super end game boss of Pokemon. And if you beat him then that makes you the Champion until somebody else comes along to try and knock you off your throne. At least, that's how I that would be the next, logical real world conclusion.

[Since there are multiple players involved here, after all!]

But not quite. I have all the Johto Badges, but only two of the eight Kanto badges so far.