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Atsumi, 厚み, is a japanese go term meaning "(the influence of) strong stones". We translate it into English with the word thickness. In order to be thick, a group of stones must be strong and it must have influence in a certain direction. See also /Atsui.
Thickness, strength and influence are often used as synonyms of each other, hence the discussion mentioned above.
A strong group is a group with no defects: the stones belonging to the group are connected and have sufficient potential for eyespace. Strength is the local property of a group of stones to stand on its own, the ultimate strength being the group living regardless of what the opponent plays in the neighbourhood.
Each stone has a certain influence on the board. Captured stones have an influence close to zero. Surrounded stones that make a live group, influence only the surrounding group. Stones that are in open space have an influence on that open space and the stones bordering that open space. Influence is a long range effect. For example: a ladder breaker changes the balance in the opposite corner.
In Go, maintaining the balance of territory and thickness is very important.
Further reading and discussion
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