In AL context, HC means "hardcover". It is used in the context of adventures published under the code DDHC. More details on which types of adventures exist can be found in the DDAL FAQ, p. 2, under What Counts as an Adventurers League Adventure?, where it explains
DDHC “Hardcover” Adventures. These adventures are officially produced and published by Wizards of the Coast.
It should be noted that it does not necessarily mean "books published in hardcover format". Lost Mine of Phandelver, for example, is not a hardcover book (at least mine isn't), but is a hardcover adventure under the code DDHC-LMOP. You could also play online with the adventure bought in DNDBeyond, for example, which wouldn't be a hardcover book.
If you are interested in playing in AL and is getting lost by so many acronyms, don't worry, Wizards got you covered. The DDAL FAQ has an acronym list on p. 3 that spell out most of the relevant acronyms that appear in the AL documents.
Hardcover adventures work differently from other adventures in many ways, this is why it's often stated "since this is a HC" or "because this is a HC". A few differences are listed below. The text with further explanations can be found in the footnote.
- Downtime and Renown. Hardcover adventures reward downtime and renown based on actual play-time, while other adventures award it based on a fixed prescribed play-time. 1
- DM rewards. Similar to Downtime and Renown, HC adventures reward the DM with XP differently from other adventures, based on the average level and actual play-time. 2
- They can be played/are played by chapters, instead of the whole adventure. 3
- They can be played by characters of higher levels if the character started the adventure within the correct range and leveled out during the adventure. Check this question for an example and explanation. 4
1 DDAL DM Guide, p. 5.
Players earn renown at the rate of 1 point per adventure (or 1 point for every 4 cumulative hours of play for Hardcover adventures).
Characters earn downtime at the rate of 5 downtime days per 2 hours of prescribed adventure length (or 5 downtime days for every 2 cumulative hours of play for Hardcover adventures).
2 DDAL DM Guide, p. 6
Dungeon Masters receive XP for every session, calculated in one-hour increments according to the optimization level of the adventure (or average party level for Hardcover adventures). This XP earned according to the prescribed duration of the adventure (or length of the session for Hardcover adventures).
3 DDAL FAQ, p. 2. This is also referenced in many other places in the form of ("when you finish an adventure or a hardcover chapter").
Players are allowed to play an adventure multiple times, but a character may only participate in a given adventure or hardcover chapter once.
4 DDAL FAQ, p. 12.
These [hardcover] adventures typically use the following ranges and can be played by characters of a higher level, provided they are within the adventure’s level range when they begin playing the adventure. A character is only “playing” one hardcover adventure at a time. For example, a character playing CoS that jumps into an SKT game, and levels outside of CoS’s level range can’t play CoS anymore. This rule only applies to DDHC adventures. Similarly, if an adventure directs you to run a specific portion of a different hardcover adventure, that portion is considered the same adventure unless you continue playing it outside of the guidance of the first.