Currencies are always quoted in pairs, such as GBP/USD or
USD/JPY. The reason they are quoted in pairs is because in every foreign
exchange transaction, you are simultaneously buying one currency and selling
another. Here is an example of a foreign exchange rate for the British pound
versus the U.S. dollar:

When selling, the exchange rate tells you how many units of
the quote currency you get for selling one unit of the base currency. In the
example above, you will receive 1.51258 U.S. dollars when you sell 1 British
pound.
The base currency is the "basis" for the buy or
the sell. If you buy EUR/USD this simply means that you are buying the base
currency and simultaneously selling the quote currency. In caveman talk,
"buy EUR, sell USD."
You would buy the pair if you believe the base currency will
appreciate (gain value) relative to the quote currency. You would sell the pair
if you think the base currency will depreciate (lose value) relative to the
quote currency.
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