What determines the value of a certain currency?

Answer 1

Perceived relative value by people who trade in currencies. Usually, but not always, based on the economies of that country.

Answer 2

As with all economics, Supply and demand.

If there is a lot of money in circulation from a country , it has a value compared to anothers countries money, For instance US money is equal to so many Euros, and this is because people who have euros, will trade that much for a US dollar, But if the price is higher they won't buy,Sometimes other people, (like the same euro money people Here) think the US has too much debt and has an operating deficit that is too high and thinks the US will print too much extra money so it won't buy as much, so the Euro people say they will sell there US dollars and trade them for Euros, Less demand means the dollar falls and Euro Rises.

But the US can counter this fall by raising interest rates so investment in US Treasury bonds gives a better rate and attracts more capital, which must buy US dollars to Buy Us Treasuries, so the dollar strengthens,

If the economy is going well compared to the rest of the world, foreigners will buy US stocks to cash in on the economy, or buy corporate bonds, but to do this they must trade their currency for US currency and this supports the dollar. If the economy goes in the tank, people want to invest elsewhere, so they sell their stocks and bonds, get US money which they sell to get next investment in another country , so US dollar Goes down

So you can see, The dollar is a factor of suplly and demand, all currencies work the same way unless they are artificially pegged to another currency or basket of currencies