Organized Play.
D&D Adventurers League is an "organized play" system.
Playing
Local stores host games (often with volunteer DMs, sometimes with paid ones). Players play point-build or array-build characters in whatever adventure is being run. Character's experience total is tracked, and players can drop-in/drop-out on a session by session basis.
Ideally, it works best if the adventure has the same 3-7 players week after week, but that's not a requirement. In fact, that's often a problem to arrange.
A given character can only participate once in a given adventure. If a player wants to play it again, they can use a different character.
DMing
From the DM perspective, the DM gets his marching orders from the store. The store either gives him the download password or gives him the adventure to run. The DM then runs the adventure at the store in the allotted time for the first 7 players who sit down for it.
Wizards keeps track of total player numbers - they do this using the DCI numbers. The store records your DCI number, and reports it to Wizards.
All your XP is tracked on forms that you bring with, not by Wizards.
Store Coordinator
The store needs to have a coordinator - they keep track of who played, and make certain the DM's have allowed adventures to run.
At present, that's a pretty decent selection. As season 3 is about to begin, all the season 1 and 2 adventures are legal for season 3 play, as is Lost Mine of Phandelver (in the Beginner's Set). So, on day 1 of season 3, there are over 30 adventures the coordinator can choose from.
The coordinators schedule the events - there are certain restrictions on scheduling - and upload the DCI numbers of those who played in those events. They also serve as a safety net - if a player or DM is acting inappropriately, the coordinator can toss them from the event.
For full credit, events are supposed to have their results entered within 24 hours of completion. Note that, for MTG tournies, that includes the winners, but for D&D, it's just who played.
What the Various Elements Mean
Encounters: Play of the "big module" for the season in its reduced form, covering levels 1-4, on Wednesday nights at a FLGS sponsored public game. These modules are coded DDEN, and are released 1 per season. Tends to be about 10-20 weeks of play, depending upon DMing style and player behavior.
Expeditions: play of any of the expeditions modules at an FLGS sponsored public game or at a convention. These modules are coded DDEX, and there are more than a dozen per season. They tend to run 3 to 10 hours of play each.
Casual Play: Any other store or club sponsored public event use of the DDEX and/or DDEN modules, or of the hardcover big adventures, that is being reported to Wizards. Can include store reported home play, and play of the hardcover versions in store.
Epics: convention modules not available to the stores. They look to be set for 4-8 hour play blocks. The modules are coded DDEP, and while generally unavailable, leaks have happened.
Home Play: a limited exception to the program, certain modules can be played at home without reporting. It is only allowed for the hardcover modules (At present, Hoard of the Dragon Queen, Rise of Tiamat, Princes of the Apocalypse, and Rage of Demons) and the Lost Mine of Phandelver boxed set.
Note: Some of these definitions are taken from non-public sources, namely the instructions to stores on how to report events. The rest are from the Season 3 Player's Guide.
Benefits to Store
Wizards cuts stores discounts based upon total DCI number using events - Magic Tourneys and Open Play events, as well as D&D Encounters, Expeditions, and Casual Play events.
They also expect that Encounters brings people into the stores. Further, some casual players will show up to play, and decide to buy dice, minis, snacks, or even rulebooks.
Benefits to Players
You can almost always find a D&D Encounters or Expeditions game to play in.
You get to play with people before you decide to invite them to your home game.
The adventures are in fact pretty good.
Because there are numerous pregen characters, plus the option to use characters built by the basic rules (which are free online), it's a chance to have new players find the game by showing up and learning to play at the FLGS.
There also is the opportunity for community awareness. Having D&D played in public really helps reduce the stigma of D&D. When people see it is something that can be played in public, not just in the basement, it helps dispel a lot of the myths.
Legendary Dude is right, in that the nature of Curse of Strahd doesn't lend itself well to prospectively breaking it into "episodes" or "adventures." It's designed for the players to be able to meander along their own path, following such leads as they like.
But we've got lots of data from other AL materials to inform a scheme. Specifically, I tabulated the downtime and renown rewards from the twenty-three (mostly seasons 2 & 3) Expeditions modules I had on hand. These included five 1-hour adventures, eight 2-hour adventures, and ten 4-hour adventures.
All of the 1- & 2-hour adventures rewarded 5 downtime days. One 4-hour adventure also rewarded 5 downtime days, while the other nine rewarded 10 downtime days.
Most (18 of 23) modules reward 1 renown point to any faction member participating.* 13 of those 18 also conditionally reward another renown point to members of some specified factions. On average, it works out just over 1 2/5 renown points available per 4-hour adventure.
Summing this all up, AL practices would indicate the following scheme:
Award 10 downtime days per 4-hour session. Award one renown point to all faction members per 4-hour session. (Story-)conditionally award another renown point to members of 2 factions, on average, per 4-hour session. (And spread the love among the factions.)
Personally, I think that's too complicated. I've gone over to "rewarding" downtime as real time. That is, for every day that passes in real life my players earn a downtime day. (That way they've got more to play with when we have to miss a session!) I also think that's way too much renown--remember that the Expeditions format contemplated casual less-than-every-week play, the likelihood that a player would be using different characters week to week, &c. I would recommend dropping the "flat" 1 renown per session, and just stick to 2 or 3 conditional ones, as it makes sense in the story.
So, my best recommendation, after a few years of running AL games:
Award downtime as above, or as real time. Award renown points to two or three factions-worth of players, conditioned on meeting story "goals" keyed to each faction, per session.
* - the five that don't are the five linked 1-hour adventures. Each of these are aligned to a different faction and reward members of that faction 1 renown point at its completion. In other words, if we consider these as one 5-hour adventure, it's another one which gives all faction members 1 renown point.
Best Answer
Adventurers League Player's Guide (v9.2) page 3
It only allows these three sources:
Player's Handbook
section Downtime Activities below the Between Adventures heading.
These are the options provided in the Player's Handbook/Basic Rules:
Note : Practicing Profession and Researching are not used in Adventurers League game, as far as I've known.
Adventurers League Player's Guide
additional options for you to spend your downtime days:
Other campaign documents
For further details on each option, please consult their respective source (PHB, ALPG, or XGE).
Other than activities mentioned in these three sources, none are allowed.