Why should the common people care about politics and does politics actually influence our lives much?

Uh yes the common people should care about politics, and yes politics influence our lives very much. Politics affect everything that affect our countries. Directly politics affect how much our taxes are for one, whether we have health care or not, what kind of funding our schools get, whether that bad road you drive on every day gets its potholes filled in. If it weren't for politics there would not be free education up to high school, for a basic example. People not caring about politics is how terrible governments manage to retain power despite the fact that they are doing things that nobody wants. You should always pay at least a little bit of attention to politics, and not just at election time, because knowing what those politicians are up to in the middle of a term will help you make a better choice when you vote.