1. The "Gygaxian Flavor": a kitchen-sink melange of Howard and Leiber meets Vance meets de Camp & Pratt meets Burroughs meets Merritt meets Lovecraft meets Tolkien meets Moorcock meets a dozen other authors all filtered through one man's creative vision. Nowadays people think of this as "the D&D feel" as if it's something that either always existed or grew up organically on its own but in reality it was pretty much single-handedly the invention of one man -- Gary Gygax. OD&D (especially Supplement I: Greyhawk) gives hints of the "Gygaxian Flavor" to come, but nothing like what AD&D (the rulebooks, the modules, and the Sorcerer's Scroll articles in Dragon) provides. OD&D is a toolbox for creating your own fantasy campaigns; AD&D is an extended portrait of Gary Gygax's fantasy campaign, and it's immensely seductive.
2. Gygax's authorial voice: something of a Jack Vance-pastiche -- mock-erudite, absurdly ostentatious language that felt baroque and old-fashioned in the 70s and nowadays feels downright archaic and bizarre. Who else would use a phrase like "the antithesis of weal" in place of the word "evil" in a rulebook for a game?! People who don't realize that this authorial voice (and the mock-antagonistic and occasionally condescending tone that goes with it) is at least 50% put-on and spoof are missing the joke (or are, perhaps, the butts of it).
3. The inspirational essays in the PH and DMG: The PH doesn't just teach players the rules of the game, it also gives mounds of instruction and advice on how to play it well (assuming your DM is Gary Gygax and the campaign is Greyhawk Castle) -- there's tons of valuable and inspiring stuff on PH pp. 101-109 which makes you want to start playing right away. And the DMG is even better -- while it's crappy as a reference work (almost impossibly badly organized) it's great as inspiration, with Gygax taking on the role of coach or mentor taking fledgling DMs by the hand and encouraging them with all manner of anecdotes and examples, trying not so much to teach a set of rules as to instill an attitude. There are many sections of the DMG that I still re-read from time to time and draw fresh inspiration from, which is ultimately much more interesting and valuable to me than, say, a straightforward explanation of how initiative is actually supposed to work (but OTOH it would've been nice to have that too...).
4. All the Charts and Tables and Lists of Miscellaneous Crap: Reputed magical qualities of gemstones and herbs, wandering prostitutes, dungeon dressing (including weird noises and junk found in dungeon hallways), characteristics of magical substances, types of diseases and insanity, areas of expertise for sages, glossary of naval terminology, types of governments, NPC personality characteristics, the Potion Miscability Table, material components for spells, the Inspirational Reading List (I'm still pulling titles from that list 20+ years later), etc. etc. etc. This stuff is informative (find someone of a certain age who knows how to use all those Latin abbreviations (i.e., e.g., q.v., et al.) correctly and it's almost certainly a former 1E AD&D player), entertaining, and hugely inspirational -- I can still pour over these lists and tables for hours and come up with dozens of encounter and adventure ideas.
5. The Davids' (Trampier and Sutherland) Art: Sutherland's art captures the Spirit of the Game absolutely note-perfectly (and, yes, the lack of professional technique is part of the appeal) whereas Trampier's art is, IMO, still the best art ever produced in the rpg industry. Honorable mentions also to Erol Otus and Tom Wham.