Balance is a placeholder skill that has been coded into the game but which lacks a use or method of improvement. It is not associated with any labors or professions, and is a placeholder to be implemented as part of the combat overhaul underway in the next version of the game.
Toady One in a February 2013 Future of the Fortress reply:
"Balance is a measure of how much you can physically do at any one point in time. Attacks, jumps, and various physical actions put you off-balance, and the more off-balance you are, the less swiftly, accurately, and powerfully you can move or act.
Hence, the more different actions you try to juggle at a time, the more imbalanced you become. Likewise, guarding or dodging makes you imbalanced, which gives a penalty to further dodging or attacks, making subsequent dodging less likely.
How much balance any given action "costs", and how quickly it recovers could be a measure of Kinesthetic Sense and Agility (although separating out agility and dexterity may be warranted)."