An Adventure, especially in the context of the experience point awards, is a very specific thing in BTB AD&D. It is difficult to nail down a specific definition, though. The Player's Handbook describes three different types of adventures: Dungeon Expeditions, Outdoor Exploration, and Town Adventures. It even mentions,

[that] one can lead directly into another sort altogether. (Gygax, pg. 101)

An anology may serve to illustrate how I like to think this works.

Hero Manager - The Game

Imagine a computer game -- especially one from the early years of PC gaming. In this game you manage a group of adventurers. Your main screen is titled "Home Base", and from this screen you can perform all the various tasks necessary to prepare for an adventure. Each of these tasks are specific to a particular Character; ie. you would select a Character, then select a task for that character to perform.

For example, a possible list of the tasks available and their cost in time are: Bed rest(1 wk), Healing(1-30 days), Training(1-4 wks), Scroll/Potion preparation(1-10 days), Poison research(20-32 wks), Sage consultation(0-40 days), Spell research(variable), Enchant item(3-10 days), Henchman recruitment (2-8 days), etc. Each task might or might not require the Character performing the task to be unavailable for adventures during the tasks progress (most do).

After you have assigned tasks to as many Characters as you desire, you may select from a list of available adventures to participate in. When you do, the game presents you with a list of Characters currently available to adventure. If a particular Character you want to take on the adventure is not currently available, you have the option of advancing the in-game time. This can be done multiple ways: you can select a character which is currently unavailable and advance the in-game time to the moment he is available, or you can advance time a specific amount of time (hours, days, weeks, etc.), or you can select a complete party of Characters and advance time until all of them are available (which will have the effect of causing some subset of the party to be idle for a period of time).

Once a party is available, you select one of the available adventures and Go Adventuring. This mode of the game operates differently depending on which type of adventure you selected, and each type has its own screen.

A Dungeon Exploration adventure operates on a time-scale of 10-minutes per turn. You explore an map of some sort and participate in combat with monsters. Your screen displays party resources such as light sources, food,etc. Each character has individual resources, too, like hit points, spells memorized, ammunition, etc. You are similarly presented with available actions like: Explore, Rest, Cast Spell, etc. Once an action is select, you press the end turn button and the turn is processed. Messages are displayed detailing the results of actions, which might include an encounter. When an encounter occurs, you are taken to an encounter screen, which similarly has its own time-scale (1-minute per turn), list of actions, and an end turn button.

An Outdoor Expedition has its own screen, too, with a time-scale of ½-day per turn. A Town Adventure also has a screen, with a time-scale the same as Dungeon Exploration adventures: 10-minutes per turn. Each of these has their own list of actions to be selected and an end turn button.

One type of event, similar to encounters, represents a transition from one type of adventure to another (eg. You're on an Outdoor Expedition and you receive an Event Message when you press the end turn button which reads, "You found the entrance to a mysterious cave! Descend? (yes/no)").

These transitional events do not allow the Characters to return to Home Base before making the transition. Instead, they change the Characters involved from one status to another.

At any point, you (the Player) can go back to the Home Base screen. That screen would still display the Characters you left on the other screens, but their current status would be listed as "Adventuring: Outdoor Expedition - in progress" or some-such. You could, from the Home Base screen, select a party currently adventuring and rejoin their current screen, if you so desired.

Each listed Character on the Home Base screen shows their current state, as well as when they will next be available. If they are currently in the middle of an adventure (ie. "in progress"), they are unavaliable for any action other than rejoining their currently in-progress adventure screen. However, if you select the Return to Home Base action from any of the adventure screens, those Character's status would be updated to read, "Adventuring: Outdoor Expedition - returning", or something similar. Any Characters listed as "returning" are valid targets for the aforementioned advance time option; those listed as "in progress", are not.

In other words, each Character operates on their own schedule. Sometimes characters adventure together, in which case their schedules are synced.

Here is the point (wow, it took awhile to get here, huh?): Experience points are awarded to individual Characters whenever they return from an adventure and become listed as "idle" on the Home Base screen, but not before. If they transition from one type of adventure to another, (Outdoor Expedition to Dungeon Exploration, for example), they never get listed as "idle" on the Home Base screen, so you never get the "Xyz Character has received experience points!" event message. Once you do receive that event, the "Gain a level" event becomes available if the additional experience awarded is sufficient to make them eligible for an additional level.

Conclusion

I hope the above all makes sense. Thinking about a larger, overarching game taking place outside of any individual character's actions and events can help you get mentally closer to the game Gygax and Arneson were designing. To be fair, they never laid out their design ideas so explicitly. However, I believe we can infer this "meta-turn" game by the rules they chose to emphasis. For example, their are a lot of seemingly irrelevant rules which are REALLY easy to ignore if you dismiss this "meta-turn" game.

Without the meta-game, upkeep and trainig rules feel excessive and over-expensive. All of the various research, preparation, and studying rules are mostly needless and over-complicated. Crafting and enchanting rules can similarly be removed.

Here's an interesting detail you can spot from this context: If you imagine Henchman and Hirelings as additional Characters in the fake computer game above, you can see that one of their primary purposes is to allow the Player to take additional actions when primary Characters are occupied with long-lasting actions and otherwise unavailable. Is your Wizard busy for the next 20 weeks researching a new spell, but there is a goblin uprising in the Kron Hills? Don't worry, send Nodwick, your loyal Halfling Fighter/Thief and his band of merry comrades to handle the situation! Another purpose for these NPCs is filling out an otherwise too-small party when an adventure is required but some of the primary Characters are currently busy. Without the meta-game, henchman and hirelings lose much of their value and purpose.

Another entire level of the meta-game becomes clear when our fake computer game allows you to continue playing after the death of one of the primary Characters. Did Sir Galahad, the Human Paladin, die of old age after 97 years of pious life and a long and succesful adventuring career? No problem! Your Drow Elf Fighter/Ranger Drizzt is still alive, and will be for another 350 years! All of a sudden Demi-human level-limits make more sense. The meta-game would quickly devolve into Demi-human-only strategies because they would have time to do the really long-term leveling, research, treasure-gathering, etc. The long-life of the Demi-humans is now a HUGE advantage, and the meta-game designers had to balance that advantage for the Humans somehow. Otherwise, no-one would ever be a Human, or even use a Human for tasks other than cannon-fodder.

Researching the rules and slowly coming to this view of the 1st Edition AD&D Game has really opened my eyes to what must have been Gygax and Arneson's original intent, as well as a view into the reasons behind some of the decisions they made.