Well, with a slight twist on the format, for me...
- OD&D is about adventures
- 1E is about expansion (FR, DL); BECMI D&D is about pick-up-&-play
- 2E is about consistency, while continuing expansion (DS, PS, SJ, etc.)
- 3.XE is about clarification, while continuing consistency (d20) & expansion (Eberron, OGL)
- 4E is about unity, while continuing clarification, consistency, & expansion, and regaining the pick-up-&-play format
I had to include OD&D & BECMI D&D since they played a significant role in gaming as well.
IMO, OD&D laid the conceptual foundations: a band of adventurers exploring the unknown and fighting monsters.
BECMI D&D & 1E expanded on that basis; BECMI more or less kept things down to a minimum (3 ALs, simple equipment list, race & class combined into class, etc.), while 1E expanded considerably (9 ALs, seperation of race & class, % scores, new settings, etc.).
2E took the framework of 1E and made things consistent, yet familiar. It really wasn't a big leap from 1E to 2E at all, though it unified some systems (rather than, IMO, be a hodge-podge of slapped-together mechanics held together by duct tape; they were welded together now).
3.XE upped the consistency factor moreso ala d20: dice rolls had a direct, visible result instead of a conditional result (and not the "roll low = good in some cases, roll high = good in other cases" of previous editions). A clear system for magic item creation that players may be willing to use was introduced (instead of the harsh sacrifice of previous editions). Building things (monsters, NPCs, etc.) had a clear system instead of being a random jumble of numbers. And it really took the first steps of "play whatever you want" for players: no more class restrictions & level limits based on race, a single XP progression chart, etc.
All of the prior editions, IMHO, tried to claim/maintain some degree of realism with its fantasy element: those "save or die" effects, the weapon modifiers against certain types of armor, etc.
4E, as far as I can tell, continues 3E's trend, but regains the pick-up-&-play feel of older editions (esp. for me, the feel of BECMI D&D). And, I think one of the ways it does this is by embracing the arbitrary aspect of the game, and getting away from trying to replicate realism: no more "save or die", no more slow progression of healing, etc.
And, 4E evens the playing field when it comes to characters. In previous editions, fighters were the realm of beginning players—rather straightforward, and no concerns about how your abilities work. Magic use, and to a certain degree skill use, was a bit more "advanced" level of play (because it needed a certain level of awareness of those options during game play—no good playing a thief if you didn't think to check for traps, sneak, or the like). The good old fighter was the "kiddie table" of the classes, if you will.
Now all classes are the same level of ability to play (though the psion class threatens to change that, from what I can tell). No more "kiddie table classes."