Damru symbolizes the Universe which is always expanding and collapsing. From an expansion it collapses and then it re-expands. This is the very process of creation.
If one sees his heartbeat, it is not just one straight line but it is a rhythm that goes up and down. The whole world is nothing but rhythms; energy rising and collapsing to rise again. So the damru signifies that. The shape of the damru is like from expansion it collapses and again expands.
The damru is also a symbol of sound. Sound is rhythm and sound is energy. The whole universe is nothing but a wave function, it is nothing but rhythms and is just one wave (Adivata). So the damru signifies the non-dual nature of the universe.