A coffer is a small safe or lock box that's meant for keeping precious or valuable items safe.
A city coffer refers to a bank account that is being filled by fines, taxes etc.
When it comes to the saying fill the coffers it means that the city is just collecting money either through fines, raising money etc.
The money in the coffer pays for city upkeep such as streets, lights, water lines, sewer lines and pays the employees the salaries that they earn.
Years ago cities would keep money in a safe which is known as a coffer and some still do keep some money in a safe to use for making change etc when people pay their bills.
However most of the money that the city has is kept in a bank account for the city.
Just like a county coffer would be in a county treasurer bank account when you pay your taxes such as real estate taxes that money would go into a bank account to pay for services such as schools, roads, police, etc.