The metric tells you how to measure distance (for each coordinate) on a manifold. Which is quite handy in GR, as most of the time, the manifold, which represents spacetime, is warped. The metric provides you with a way to measure distance and time on a particular manifold. Remember, the manifold represents spacetime. For a discussion of metrics, go here

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.