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Atsumi, 厚味, is a Japanese go term meaning "(the influence of) strong stones". Its literal meaning is thickness. In order to be thick, a group of stones must be strong and it must have influence in a certain direction. See also Thickness/Atsui.
Thickness, strength and influence are often used as synonyms of each other, hence the discussion mentioned above.
The Go Players Almanac defines it as thickness, power, or strength, particularly facing the center or an open area.
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.
Further reading and discussion