Well, I think it really is everything that isn't a social encounter or combat encounter.
I think we can come up with a better definition that gets at what many examples of fun exploration pillar play have in common. Obviously not everything you can do in D&D besides combat and social interaction is worth spending time on, so we want to exclude some things.
The three pillars image suggests that each category has a cohesive identity. The implicit advice is that a D&D campaign is best when play is roughly balanced between the three pillars. It's essential to have some clarity about what each pillar entails for this to be useful advice.
There's another book that explains some of the more esoteric words that are used in the PHB. It's called the dictionary.
There are many terms of art in D&D that are only distantly related to the same words in the dictionary. A dictionary wouldn't be very helpful for understanding what class, level, feat etc. mean in this game.
The exploration pillar has scenery. You can't talk to mountains and you can't fight them but you can try to get to the other side through mysterious hidden passes in blinding snowstorms. Dungeons have twisty-turny passages full of strange smells and mysterious banging noises in the distance; you can't fight smells and you can't talk to them but you can wonder what they signify. Dungeons have doors you might want to open and maybe wish you hadn't. It's all exploration.
I think focusing on the scenery rather than the logical structure of exploration gameplay is exactly the wrong way to go. That would suggest that a long boxed text description of a perilous journey or dungeon crawl is just as effective for balancing a combat heavy adventure as actually exploring those things, when it definitely is not. But you might not appreciate that since by your post history you appear to primarily play D&D in the form of PbP freeform roleplay.
I think the bits you didn't bold are probably the key sentences.
I don't think the description of exploration play in the PHB is defensible; there's nothing there in any way helpful for DMing or designing fun exploration gameplay.
It's about paying attention to the DM's description of the environment and making meaningful, informed decisions by moving about, gathering information, and using that to improve your chances of success at other challenges. That is the exploration pillar in my view.
Interesting post and I think you are mostly right. I would expand and clarify in two ways though. Correct me if I'm wrong but in most of the exploration 'challenges' in your adventure your players didn't know before engaging with the challenge exactly what their goal was (e.g. "notice the shriekers"--they didn't know that there was about to be something they need to notice). This seems to me to be the salient feature of exploration play: it's about going after the unknown unknowns, as it were. By contrast in a goal-oriented challenge the players know what they need to accomplish and just have to figure out how to do it.
The upshot of this is you have a couple of challenges there which by this way of thinking would not actually be exploration challenges. E.g. stuff like climbing a well shaft safely without falling. This sort of "drowning & falling" challenge I think isn't actually exploratory, and I would like to remove it from our understanding of the exploratory pillar. Personally I think most of those suck. I think associating them with the exploration pillar has been deleterious because it's made people skeptical of the value of all exploration pillar play.
Exploration is traversing obstacles & discovering things in the environment, often things you're specifically looking for or looking to avoid - treasure & traps in a traditional dungeon crawl, which is very exploration-heavy, for instance.
As per my comments to [MENTION=97077]iserith[/MENTION] above I think traversing an obstacle and discovering things in the environment are two different sorts of gameplay. One is goal-oriented and one is, well exploratory.
I think the goal-oriented challenges that get lumped into the exploration pillar (climbing a cliff, crossing a river) mostly are not very interesting. You know where you want to go, and you need to pass some checks to get there or you drown or fall or something. In terms of the logical game structure they're basically very simplistic, boring combats and should actually compete in that category for space in the adventure.
Interaction (or 'social' - NOT 'RP,' it's all RP), is any non-combat interaction with other creatures to achieve a goal (or avoid a problem, like combat).
So you think social interactions aren't worth playing out unless the party has an explicit goal? I wouldn't agree with that. Another aspect of my confusion here is that many social interactions seem to be exploratory rather than goal-oriented. Or even neither, and purely for the purpose of "role play"/thespianism (possibly a fourth pillar, although I'm not a huge fan of this myself).
It's well worth noting that both Interaction and Exploration can easily lead to combat. Negotiations break down, there's a fight. You disturb an undead's tomb or touch the item a golem is guarding in the course of your exploration, there's a fight. Thus combat is often viewed as the most-important or more prevalent pillar or the pillar of last resort.
I would point out that combat can break down into exploration (fleeing into unexplored parts of the dungeon) or social interaction (parley/surrender). And social interaction to exploration (if you offend the wrong person and get teleported into a maze, or banished to the Isle of Dread).