Why exercising the right to vote is citizen's fundamental duty?

In a democracy (that is the system where people have the right to vote) the power is with the people. However, it would not be feasible to let people vote over all the laws directly: so this is done by the representatives.

The representatives have to be chosen, and they have to be chosen well for the democracy to work well. So the answer is: it is neccessary to vote to make sure that the country functions well!