It is a government-controlled currency. The medium represents economic power.
It is also reasonable to assume that in TBS games, money in itself also has a certain amount of GOLD or SILVER or another valuable metal inside. This prevents individual kingdoms from flooding the market with currency. On the other hand, it tilts the balance of power to those who have access to the metal - even if it has no direct function in itself.
It is also reasonable to assume that in games where multiple currencies are used (gold, silver, platinum, copper), the exchange between these currencies is fixed, and thus has to be backed by an organization that either limits or encourages the spread of unbalanced metals.
As the player in a TBS game, currency primarily purchases labour. Secondarily it purchases materials.
I think it makes perfect sense, in a computer game environment. If an organization finds itself in a situation where it can use an obtained resource in exchange for other things it desire, it will do that if the exchange is reasonable. In this case, gold purchases prosperity, and the exchange is very favourable.
If you're looking for a deeper explanation than that, then I think you should more closely examine why gold is, and has always been, a desired metal in human civilization. You might also want to read some introductory national economics or even economic history to understand how the view of currency has changed over the years, but gold has maintained its value.
I think it is important to think of gold as never leaving the system, in a TBS game. If you spend gold, the money is not consumed. It remains in the society, used by individuals to pursue their desires. The gold eventually circulates through the system. Thus, there is a huge difference between what currency you, as a player, have in your hand - and the accumulated wealth of the society you are constructing. However, only the currency is readily available - the rest is tied up.