I think this question is best explained with a demonstration. In this case I'm playing a Range puzzle, but this kind of concept seems to work with other puzzle types too.
Of interest here are the two blank squares in the last row of the puzzle. Let's call the left of the two blank squares A, and the right B.
If square A is black, then square B must be white, since two black squares cannot be orthogonally adjacent.
If square A is white, then square B may be white or black, and the puzzle would still be in a valid state. No other restrictions are placed on square B.
Therefore, square A must be black, to guarantee a unique solution to the puzzle.
My question is, when solving puzzles, is this kind of logic sound? If I follow this logic through in other contexts, is it always guaranteed to produce a correct conclusion? Is there a name for this kind of logic?