[Typically, when we say Session, we mean an entire "sitting" of play, an evening (or other part of the day) of gaming.
I've been thinking/advocating shorter sessions for a while. Instead of the monstertruck 4 hour session of play, play for two hours, take a break, then play for two more hours. Apocalypse World (I'm tired of referencing this game!) with its end of session moves is useful as a test subject for these kinds of things. When you're playing online (PbP) you need to arbitrarily decide when a "session" has ended, so people can adjust their Hx. When I played with Vincent at Lucca, we took a 10min break in the con game for similar purposes. Breaks can be good. They let you clear your head, think about the game, go to the toiled, smoke a cigarete whatever. You can refresh your gaming energies and then jump right back in. They can build suspense (cut at an important point). They can give space to out-of-character, person-to-person feedback that's sometimes hard to get in the middle of actual play.]
This game I'm working on requires some mechanical dice fiddling and stat adjusting that is not directly related to the fiction but will influence the fiction from there on (broadly speaking: it's like getting XP/leveling up in D&D). Initially I placed this procedure at the end of play, or more accurately, end of the session. But I think that might be too slow, because you don't get to see how your character changed until next week (or whenever you're going to play next).
So I want it to happen in the middle of the game. But it definitely shouldn't happen too often, so not at the end of every scene. So Middle of the Session is a good place for it. But I don't know how to measure that time (if you don't know how long exactly you'll be playing) or what to call it (chapter? act?).
Let's say that a session contains two or three Acts, what's a good, hard rule for when to close an act? Something like "An Act lasts X number of scenes" might do, but my game doesn't use Scenes as a resource strictly speaking. D&D 4E has "milestones" which is every two Encounters or something like that if I remember correctly. Any other ideas?