Who has surrounded more territory - black on the outside, or white on the inside? This was an "aha!" moment for me when I first saw this question and heard the answer. Black has claimed 136 points on the outside and believe it or not, white can only claim 121 points on the inside. The point is: the outside of the board is very valuable!
Not only are there a lot of points available at the corners and the edges, they are actually "cheaper" to surround.
Above we have 3 groups of stones, each group surrounds 9 points of territory. Look how many moves it takes to get 9 points in the corner, on the side, and in the middle. You have to work twice as hard to get the points in the middle (12 stones) as compared to the corner (6 stones). Capturing territory on the side is right in the middle in terms of cost (9 stones).
These 2 "facts of geometry" on the GO board should help you see why it makes sense to try to claim the corners first, then the sides, and finally wrestle for the middle.
Interesting sidenote: 19x19 is the largest board one can have where the outer 2 rows are more valuable than the points inside the 4th row. I guess the game would play differently on a 21x21 board!
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