One repeated observation of amateur play is that amateurs fall into the trap of assuming that each move must be significant in itself - make a threat, defend a weakness, etc. Master play is significantly deeper in recognizing that a move may be used in order to prepare a much greater threat, set up a combination, and so on.
One of the more subtler concepts that I've run across, and it is perhaps more valuable to recognize because of its subtlety, is clearing squares for pieces. The piece that is moving is therefore not the significant actor in the chess drama, it is the piece that will replace it on the square. This may be an obvious concept to many, but for those of us who too easily overlook ideas or valuable candidate moves, the insight can help our thinking and give us an extra edge. It can also be a combinative idea or a positional one, so it has broad applications.
Chess being a practical game, here are some illustrations of how this mastery concept can work in practice. Chesstempo also has an illustration of a piece clearance sacrifice as part of its reference on tactical motifs.
1. Ernesto Real de Azua - Vinay Bhat (2000)
This game was highlighted on GM Bhat's There and Back Again blog and was included in Daniel Naroditsky's Mastering Positional Chess (New in Chess, 2010). The next move in the viewer (19...b5) dramatically paves the way for ..Nb6 and gets Black out of a serious jam. The link above has more of GM Bhat's analysis and commentary.
2. Alexander Chernin - Anthony Miles (1985)
This is a classic modern game featuring a pawn sacrifice in what Hans Kmoch in Pawn Power in Chess termed a "sweeper-sealer-twist" - the pawn is moved (sacrificed in this case) in order to replace the pawn with a piece on the square. Here 12. e5! is the move that the rest of the game revolves around, as the e4 square is pivotal for White.
3. La Bourdonnais - McDonnell (1834)
A classic historical game that shows how effective clearing a square for another piece can be.