That valve looks pretty old. In any case if the handle turns 90deg. and the result is the water is not shut off the valve is defective and needs to be replaced.
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That type of valve has a ball with a hole in it. The ball is rotated so the hole is either inline with the pipes or 90 deg. to the pipes allowing the water to flow or to be stopped.
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The ball is attached to the handle with a rod. Often the ball and rod are one piece. Over time the rod becomes weakened with corrosion and the ball becomes stuck with mineral deposits. When the handle is turned the torque breaks the rod and the ball does not move. The result is you believe you turned the valve off, but you have not moved the ball to block the water...so it still flows. The only option is to replace the valve.
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