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It depends on which systems of foreign exchanges one is talking about.
Assuming it is a largely market system, that is, everyone can buy and sell at the market rate at any time, then it is the demand and supply of a foreign currency. This has little to do with gold reserves, although gold reserves can be considered as some equivalents of foreign currency reserves. It is related to economic conditions, but that is only one of the factors.
To put it plainly, exports increases the supply of foreign currency and imports demand it. Capital flows are also important factor.
Exchange rate is generally affected by stage of economic development, largely through trade and foreign investment effects. When an economy is under-developed, its products are seldom competitive internationally. There is an effect of "brand". Even the same products can have different prices if they are from different countries. If they are from a developed country, the prices are likely to be higher, because people trust them more. Maybe that is a demonstration effects, or a risk premium for not well known products.
There are other factors too, but they can all be summarised in the demand and supply framework. Of course, even in free exchange countries, the central bank can intervene to affect the exchange rate, at least in short term.
For other fixed exchange systems, that is a different story altogether.
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