In EUR/USD, the euro is the base and the dollar is the quote-currency. A price of 1.0850 means one euro costs 1.0850 dollars. Buying the pair means buying euros with dollars; selling it means the reverse.
Lot sizes are counted in the base currency: a standard-lot of EUR/USD is 100,000 euros.
Example: buying 1 standard lot of EUR/USD at 1.0850 means you now hold 100,000 euros and owe 108,500 dollars.
Related: quote-currency, major-pairs, standard-lot, pip