Exchequer is a British term for the individual in the government who is in charge of the money: the treasurer. Sometimes it refers to the office in which all the money is kept, the treasury itself.
If you follow British government, you may have noticed that although they have a democracy much like ours, some things are very different. One of them is that the person in the government who is in charge of the government's finances, the Treasury Secretary, is called the Chancellor of the Exchequer. The word has been around for a long time. There were exchequers in medieval England, back when exchequer offices worked for kings.