Republic (noun)

1. A state in which supreme power is held by the people and their elected representatives, and which has an elected or nominated president rather than a monarch.
2. A state in which the head of state is not a monarch and the government is not hereditary.

Origin:

Late 16th century: from french république or latin respublica, from res "thing" + publica "public".

Examples:

1. The United States of America is a republic.
2. France is a republic.
3. India is a republic.
4. Brazil is a republic.
5. Australia is a constitutional monarchy, but it is also a republic in the sense that the head of state is not a monarch.