I believe up by 1 point means that the possition is such that you are up something about equal to a pawn be it an actual pawn in an otherwise equal possition or a possition where you are possitionally better enough that you'd have been willing to sac a pawn to get there. (It could also mean you are up a piece but your opponent has some possitional compensation)
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How do we know much of an advantage one side has when the computer gives scores based on position? I think that 0 is totally drawish, 0.1 is a very minor insignificant plus, 3 is a good plus, 7 is a moderate advantage, and 93.05 is a queen up in the endgame against a bunch of scattered pawns and nothing else but a doomed king.