идиома ≈ без единой царапины; свеженький, как огурчик
example
"Surprisingly, given that it had been run over by first by a milk float and then a large removals van, Mark's briefcase appeared none the worse for wear".
"Despite his prodigious vodka consumption the previous evening, Vladimir arrived at the breakfast table at half past eight, apparently none the worse for wear."
"Not the worst for wear" (or more commonly, "None the worse for wear") means: "Not perceptibly damaged by recent events" (or, less confidently / assertively: "Relatively unscathed by recent events").