Thick stones are stones that have a strong formation. They cannot be easily cut apart. They usually face an open area of the board. These stones radiate influence over that area.
In Attack and Defense, by Ishida Akira and James Davies, they refer to thickness as power. Thickness, influence, and power are all related concepts.
The most important concept to remember is this:
Thickness is used for fighting. It is not used to surround territory.
In this example, Black played in the upper left to make a wall. This wall is thick. It does not have cutting points, and it radiates influence down the left side of the board.
Later in the same game, White invades at the bottom of the board. The marked white stones do not have enough room to live, so they need to run. It is made harder by the fact that they are mostly cut off from the rest of the board. The thickness in the upper left of the board allows Black to attack the group in the lower right more strongly.
Black can attack with . The marked white stones look like they are in trouble. They need to run to the center, but they are being pressed against the strong black group on the left, and being herded towards the thick wall in the upper left.
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