Most birds have the Vitali Organ, a unique middle-ear receptor that can sense minimal fluctuations in atmospheric pressure.  But, with extreme sensitivity comes equal pain reception.  So, the quicker atmospheric pressure falls (indicating an approaching storm), the more birds will fly low (and the lower they fly) to the ground in an attempt to alleviate the discomfort caused by the pressure change in their ears at the higher altitudes.

Birds do not have to be flying to escape the pain.  If you observe a sudden and sharp increase in activity on power lines, there is a good possibility that a storm is bearing down on your location.  Conversely, the weather is most likely clear when you see that the birds are flying high up in the sky.
What else should you look for?  The height at which birds fly is not the only way to use their actions to try and predict the weather.  With a storm approaching, seagulls will take a break from flying and seek refuge somewhere along the coast to wait out the bad weather.  All birds usually become exceptionally quiet right before it begins to rain.
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So, while birds may not predict the weather, they are still helpful and practical meteorological aids.