two councillors can stand for each ward

Mostly in the United Kingdom: Councillors hold regular surgeries in their ward so that members of the public have regular opportunities to speak with their Councillors about any Council problems or issues that they have.

The councillors elect mayor in the municipality in India. the councillors are elected by the general public.

Initially it was hereditary kings, replaced by oligarch aristocrats who shared places on the ruling council, then in democracies by citizens who formed the assembly and councillors and magistrates appointed by their tribes.

Government of the affairs of counties, towns, etc., by locally elected political bodies.
It is run by the local councillors. People who want to be councillors are called candidates. People over 18 vote for new councillors.