Depends on the opening. Any piece that's as useless as the light-squared bishop in the French Defense is important in that it needs to get into play sooner or later. Compare Black's light-squared bishop to his dark-squared bishop in the Sicilian Dragon, though - Black often gives up a rook to keep the latter.
Why is the light-squared Bishop strong for Black?
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This sounds bit strange. Could the real meaning be that activating the light squared bishop is very important for black in the French? As far as I know in many variations of French the activation of this bishop is blacks biggest strategic problem.
In general, these things of course always depend on the particular position. especially the pawn formation greatly affects the bishop.
I heard it explained thus: "white's king initially resides on a black squareand after both kingside and queenside castling it still resides on a black square. The reverse is true of the black king."
I personally think the difference between the colors of the bishops is negligable in the french(just the color of the bishop not the "badness") However, in, say the italian game, it is meaningful.
I've seen several commentaries on openings where the commentator points out that the light-squared Bishop is a very strong or important Bishop for Black (especially in commentaries on the French Defence, where that Bishop is being blocked), but I haven't seen anyone explain why. So, why is the light-squared Bishop generally considered to be so important for Black? And is the opposite true for White? That White's dark-squared Bishop is generally going to be very important compared to the light-squared Bishop?