What is exchange rate in economics?

The PRICE at which one currency can be converted into another. Over the years, economists and politicians have often changed their minds about whether it is a good idea to try to hold a country’s exchange rate steady, rather than let it be decided by MARKET FORCES. When CAPITAL can flow easily around the world, countries cannot fix their exchange rate and at the same time maintain an independent MONETARY POLICY.
To get the best of both worlds, many emerging economies have tried a hybrid approach, loosely tying their exchange rate either to a single foreign currency, such as the dollar, or to a basket of currencies.

An exchange rate is the Value of a currency required to buy a unit of another currency.

So lets say you are an English Man from London and want to exchange British Pounds for Dollars and the exchange rate reads GBPUSD 1.7558. It simply means you that 1 GBP(British Pound) to get 1.7558USD (US Dollars).

where GBP = the Base currency (domestic)

and USD = the Term Currency(foreign)