The British philosopher John Locke once made the case that the human mind is best described in terms of "ideas", and I think the same holds true for chess. People talk about tactics and strategy, theory and calculation, opening principles and endgame mechanics, but what all these terms boil down to eventually is ideas.
Think about it. The single most important thing about each and every chess move is that you know what you are doing, regardless of whether you deal with a tactical move, a strategic move, an opening move, an endgame move, an aggressive or a defensive move. And unless you excel at calculation, your decision will likely be based on an idea you are already familiar with from your previous games or your chess study.
Knowing what you are doing is key in chess, but in order to know what you are doing you first have to come up with an idea about what you could be doing. The more chess you play, the more ideas you will have, and the more familiar some ideas will be to you.
Familiarizing yourself with ideas will help you get ideas during the actual game. The nice thing about the word "idea" is that it avoids the somewhat artificial distinction between tactics and strategy. In chess, tactics and strategy are in essence the same thing: finding moves that make sense. The fact that tactics tend to play out in one to five moves rather than ten to fifty is irrelevant to the actual game: unlike a chess puzzle, a chess game doesn't tell you that there is a tactic in the position; if you want to discover a tactic in an actual game, you first have to get the idea that this kind of position might offer tactical opportunities you can take advantage of. Therefore, tactics is in essence the same as strategy, i.e. assessing the position as a whole to get an idea what kind of move you are looking for. And kinds of moves are what ideas in chess are all about.
Ideas, or kinds of moves, are the repertoire of the experienced player. They are part abstract (in the form of a motto, or principle, or rule of thumb) and part concrete (in the form of familiar positions or piece setups from previous games or puzzles). Learning a chess idea means to know the theme of the move, that is how it relates to other ideas and when the move usually occurs (in the opening, in a cramped position, in a kingside attack, in an endgame, etc.), but also to have a rough picture of the move on the actual board (knowing common positions, and the pieces and squares commonly involved).
The reason I'm waxing philosophical about the notion of "idea" in chess is that I find it highly useful for structuring and managing my study of the game. First of all, I no longer have that disconnect between studying tactics versus strategy, or or studying the opening versus the endgame; I still use these distinctions, but they are now all subsumed under "ideas", which I find makes accessing them much easier. Secondly, it is much easier for me to make sense of and articulate to myself what I am learning. When I learn, say, the 2-pawns+rook versus rook endgame, I know that I have to learn the ideas behind the moves, and that makes it much easier to look for those ideas, for instance the idea how pawns can shield a king from enemy rook checks. Thirdly, I feel I have a better grasp of what is important to retain from a study session and what is not. When studying master games, for example, I know longer care about the concrete moves or how the game progresses, but the central ideas the games illustrate. When doing tactics puzzles, I try to make a mental note of the ideas the tactics involve and the positional features that make the tactic work; just solving the puzzle, on the other hand, doesn't seem to benefit my OTB play all that much, because I can take nothing away from it except the fact that I solved it.
To sum up: The notion of idea enables you to ask, "what's the key idea behind that move, or what kind of move is this?" I, for one, find that question extremely helpful, although I perhaps need to flesh out in some more detail how I think the answer to that question should be structured. That's for another post.
Edit: Rather than writing another post, here's an illustrative example of a puzzle position. White to move:
Since this is a tactics puzzle, we already have the idea that there is some forced sequence here White can exploit to get an advantage. If we came by this position in an actual game, we might consider moves such as Re2 (defending against potential intrusions on the second rank) or Nc5 (placing the knight on a nice outpost). But as it is, we immediately start searching for a forced line, and the one forcing move that jumps out is Nc7, attacking the rook. From there, we have to calculate and see if there's a follow-up move that wins material. However, ideas are extremely useful to aid us in our calculations. During my calculation, I saw that the Black knight on d6 was pinned once the knight moved, and so I immediately considered Ne8. I also saw that Nxe8 was forced. At this junction, however, I had the idea that after Rxe8, the bishop on f8 would be pinned that that there was nothing to prevent my bishop from attacking the enemy bishop again if I moved it do d6, and I had the vague idea that Black's white-squared bishop was pinned. What I missed, however, was that the white-square bishop isn't pinned at all, and that Black can simply move his rook to a8 and after Rxe8, the bishop can move to b7, protecting the rook and his black-square bishop at the same time.
Now, you might say that this is just trivial calculation stuff and hasn't much to do with ideas at all. I would argue, however, that missing the bishop-bit in my calculation would have been much less likely if I had been familiar with that kind of bishop-move. Why? Because calculation is only partly figuring out a move-by-move sequence; a huge part of calculation is simply knowing a typical kind of move sequence. Look at the following position, for example (Black to move):
If I reached this position, I'd quickly see that Bxa4 is a bad move because after playing a lot of painful blitz games I have absorbed the idea of the rook-piece-rook pin. So it takes much less time to see that after Ra1, Black loses the bishop or the exchange. And the same goes for the above position once you assimilated the idea of rook-bishop-rook-protection. Here's the idea in its pure form:
To return to my original point: in order to absorb and retain chess positions in a way that is useful for improvement, think about them in terms of ideas. Of course, I am only a 1650-player, and I have yet to prove with my own chess-development whether the notion of idea is indeed a useful one. Let me know what you think!