The first currency in a pair (e.g. EUR in EUR/USD), representing one unit against which the quote currency is priced.
In EUR/USD, the euro is the base currency. A quote of 1.0850 means one euro buys 1.0850 US dollars. When you buy a pair you are buying the base currency and selling the quote currency.
Identifying the base currency matters for calculating pip value and for understanding which central bank's policy is most likely to drive pair direction.