Etymologically it's that which circulates or flows around within a population
We've taken this to mean money, typically commodity money — some useful good (like metals) against which other goods' values can be measured
It could also be said that words or symbols are currency, they flow between people, they are common recognitions of things outside of both parties, some third thing, some measuring stick of reality
A currency is like a Master signifier in this way
Debt: The First 5000 Years is a good book about the history of debt, currency, and money (all three of these are basically the same thing)