Often known as OD&D, but on the tin it's just D&D, no number, no "Advanced," no hint of any other game that was or will be. This isn't a game I've played, and indeed my knowledge of it is based mostly on Swords & Wizardry and hearsay. But even that gives me enough to know that this game is different in many ways from its descendants, and it has its own variation on the basic D&D core activity.
In OD&D, there's none of this "you get XP for challenges" nonsense. You can get it from killing monsters, though they're usually not worth the trouble, even if your DM includes bonus XP for special powers instead of basing it exclusively off hit dice. Instead, the main source of XP is treasure.
Thus, the dungeon. Even 4th Edition gives a few nods to that classic adventure location, since it provides a convenient source of clearly defined areas full of interesting terrain, but OD&D lives it. If the standard set up is to get XP for "overcoming challenges," or even just fighting monsters, there are plenty of other places to get it. But the dungeon, as traditionally defined, is just about the best place anywhere to find a lot of treasure. (Unless you're running an Ocean's Eleven style palace heist game, which could be fun. Make it a single race party and call it "Ocean's Elves" for maximum player irritation.)
Leveling also provides a slightly different reward than in the more recent versions of the game. True, wizards and clerics get spells, but not as many or as often, and fighters don't get any powers except from magic items, which are in turn much less common. (Monty Haul campaigns notwithstanding.) In the style the game is intended to be played, player cleverness does what modern games do with skills and feats, and the game tends to stay more down to earth. What leveling up does provide is a measure of survivability. A few more hit points, a slightly better chance to hit, and now your character can stand toe to toe with a goblin for more than a round.
But even without getting a whole lot in the way of neat powers, OD&D is still fun. It spawned a hobby, and is still played to this day. This is largely because the activities involved with gathering XP -- outwitting traps, solving puzzles, fighting monsters -- are fun in and of themselves. Later editions shifted XP a little more away from "scorecard" and a little more towards "currency for cool things," but even they depend on the fact that getting that XP is fun.