Question

What does it mean to be a part of a republic?

Answer 1

To be part of a republic means to live under a republican form of government in which a select group of leaders govern rather than one powerful monarch.

Answer 2

If you're a citizen, it means government must, in some sense, at some interval, seek your consent for its actions, e.g. by its leaders stand for election in which you vote. If you're not a citizen, it doesn't mean squat.