Every forex price is a ratio between two currencies written in a fixed order. EUR/USD at 1.0840 means one euro buys 1.0840 dollars. The first currency is the base-currency, the second the quote-currency, also called the counter-currency.
The market keeps the order conventional rather than logical. The euro is quoted ahead of everything, then sterling, then the Australian and New Zealand dollars, then the US dollar, then everything else. That is why you see GBP/USD and USD/JPY rather than USD/GBP and JPY/USD.
Direction follows the base. Buying EUR/USD is long euros and short dollars at the same time; there is no way to hold one leg on its own.
Example: EUR/USD moves 1.0840 to 1.0890. The euro gained 0.46% against the dollar, and one euro now costs half a cent more.
Related: base-currency, quote-currency, counter-currency, direct-quote