The word "saturation" makes me think the term probably means something like "they've invented all the plots they could invent in that genre" which I don't agree with. When I say I'm tired I just mean I've seen too many of them lately and would like not to see more until some time has passed.
No, when I say saturation, that's exactly what I mean. The point where there's just so much of a thing around that people get sick of it or start to avoid anything that seems to be in that genre until they've had a bit of a break and it feels fresh again.
There's kind of a curve...you know. A thing in a genre gets popular, suddenly more things in that same genre get popular because people are looking for stuff like the first thing... until that reaches a saturation point and interest drops off.
There's some debate, though, as to whether or not this happens because everyone tries to chase the success of a popular franchise or if people just become hyper aware of stuff that's already out there once they're keyed into a genre. Like with vampires... ...Twilight didn't necessarily cause that much of an uptick in vampire anything, but the success of Twilight (And True Blood, etc.) made everyone hyper aware of anything vampire related... ...and a lot of dreck got more attention than it probably would have because it was in the right place at the right time.
Not to say people never try to chase whatever is "in," but by the time you make something to try to ride the wave of something popular, that moment is usually over.
It's just something I think about now whenever the topic of "I'm just getting tired of [THING] right now..." or "There are just too many [THING] movies/books/games/comics" comes up.