What separates democracies from all other types of political systems is that government is based on the consent of the citizens. That means that the people and parties who run government are elected by us, the citizens. In turn, this means that we take the time to vote and select those candidates or parties who they think will do the best job in running the country, and in representing their opinions. People should vote for the following reasons:

You should vote, because you care about the future of your country.
You should vote to support the current government or alternatively to support the opposition if you believe that either a strong opposition or even a change of government is necessary.
And you should vote, simply because, in a democracy, you can.