The word coffer means a strong box or safe that holds valuables and money.
A government coffer is basically just a bank account or savings account where all the money that taxpayers pay goes into.
The government coffer is not just a safe but instead a bank account where all the money collected from tax payers goes into to fund the government operations.
For example your city or county has a coffer where the money you pay in property taxes goes too and then that money is spread around to fund things such as roads, fire departments etc.
So government coffer is just a bank account.