I often say things on my posts like, "Fun session." Often after a loot-free fruitless delve with no exploration and lots of frustration for the PCs.
It would be a contradiction except for the fact that "fun" isn't defined by in-game success or by the characters.
So what is the fun in our fun?
For me, it's a combination of these:
Exploration/Discovery: I really enjoy sessions when the PCs go new places, or find new things. Or better yet, gain understanding of something I've had to keep under my hat for a long, long time . . . and then I get to watch them figure it out.
Reward: The PCs finding something rewarding - or the players learning/earning something rewarding, is fun.
NPC-PC and PC-PC interactions. These are especially fun if the NPC is interesting to the PCs, or the PCs have to deal with language issues, cultural confusion, or suprise the NPC with unusually non-PC actions (such as: reasonable payment, trust, not lying to them, not killing them because of legalistically argued reasons, or even attempted friendship). Those are a lot of fun. Watchng the players try to figure out how to deal with a given NPC, given their own issues and goals, can be amusing. In-game obstacles being overcome to get these interactions makes them more interesting to me.
The players. These is the main bit, really. It's why a 10-12 people game is fun even though we can't get much done. It's just awesome hanging out with an extendd group of people we all enjoy gaming with. (As much as the players say, "We need Dryst!" we'd be perfectly happy with Angus McSwashy . . . we're really saying, "We need A____" - the player, not the character.)
If these are there, at least in some portion, it's usually a fun session. Notice that combat isn't there. A good fight can result in good stories, but generally it's really a fun fight if something interesting happens that's more rewarding than just killing some monsters. "Loot" is a subset of "reward." "People getting to use their cool powers" isn't there. It's moving around the sandbox, interacting with elements, figuring it out . . . and doing so with people you like to spend time with. Those make for good sessions.
Equally, you can have some bad from the above. Lack of exploration. No reward, and no one learns anything. NPC-PC interactions are the usual flawed negotiations and full of lies and scheming from characters incapable of sustaining either - Conan the Cimmerian trying to be Cugel the Clever. And players not being able to make it. Even a small group is fun, but a large group is better.
That's where the fun lies in my games.
It might be a bit different for my players . . . but we've had a blast in some of the sessions where the summary indicates a total non-starter of a session. So I expect we'd have a very close overlap if they chimed in.