Simple Definition:

A republic is a system of government where the people elect representatives [people chosen to act on behalf of others] to make decisions on their behalf. In this system, the laws and policies are created by elected officials and not by a single leader or monarch.

For example, the United States of America is a republic where citizens elect their President and members of Congress to make decisions for the country.

Very Simple Definition:

A republic is a type of government where people vote for leaders to make decisions for them.

For example, in a republic like the United States, citizens vote for their President and Congress to make decisions for the country.