Again, posting my thoughts before reading others..
Things in common to all editions
Adventure: Archetypal fantasy characters that explore strange—mostly underground—places, encounter odd beings, and get into a lot of battles with them;
In a Game: While it may have some (or more then some) narrative and simulation, is still a game;
From familiar Fantasy: Massive borrowing from history, mythology, and fantasy fiction;
But with Its Own Style: These borrowings are then warped into D&D shape, and supplemented by even stranger D&D-isms;
And still Flexible: AD&D still gave DMs and players a lot of freedom to put their own spin on things. To put the flesh on the bones, as the DMG said.
Things specific to AD&D
Style: Its not for everyone, but the attitude and style of 1st ed (through about 84-86) remains something approached, but basically untouched. Sure the art is technically better, something’s make more sense, but neither of those creates style by themselves.
The Adventures: These where the stars, and deservedly so. The 3rd edition era also has some gems (out of a much larger number when 3rd parties are included), as do those other editions of D&D, but again, style, the details, the execution, and the way they worked in play, mostly great.
Scope: earlier editions of D&D seemed a little light. And later would come the bloat. Put those first books, with their range of classes, spells, items, and monsters, still feel about right. And if you want more: your module will probably have it.
Play: worked in practice: I hammered AD&D for its rules in another thread, but in practice it worked. And its important to keep in mind that there were worse ideas—many of them—in the early D&D supplements and Dragon that where not put in. For all its flaws, it remains more playable (esp. once the old D&D “common law” is added) then many other role-playing games.