High or low
When playing in an undeveloped part of the board, one faces the dilemma of playing to secure more territory or to gain influence over the rest of the board (this dilemma could be equated as "Influence Or Territory").
Most plays in an undeveloped area (including the opening moves in the corners) will be played on the third or fourth lines. There is a tension between these lines that is one of the challenging aspects of the game.
The third line is the "line of territory"; plays along this line will encompass a good amount of territory but will be difficult for the opponent to invade. However, this is at the cost of reduced influence over the rest of the board; the opponent can easily "cap" the third line stone with a play along the fourth or fifth line. Third line plays (and below) are "low".
The fourth line is the "line of influence" (for different reasons, it is also called the "line of victory"); plays along this line are too far from the edge to secure territory well, but have a large influence on other parts of the board and the fighting that will occur there. Fourth line plays (and above) are "high".
Thus, a pincer played on the third line is a "low pincer", and emphasises territory; an extension played to the star point on the side (fourth line) is a "high extension". It is a challenge of the game to keep the balance correct between low plays and high plays in a game.
-- BenFinney
See also:
A Japanese ex-insei told us to think of third line plays as stabilizing and fourth line plays as developing. This a different way of thinking, which is not the same as saying the territory/influence reasoning is wrong. Interestingly so, he also modified a well-known proverb into "Don't play (develop) close to stable groups." --Dieter
The more I play, the higher the fourth line seems to be. ilan