In stocks, bullish means that the price of a stock is going up (or you think it will go up). Since forex is traded in pairs, bullish means the price of that pair is going up (or you think it will go up). If you are bullish on the EUR/USD, you think the EUR will go up vs. the USD. This makes you bullish on the Euro and Bearish on the US Dollar.

A candlestick where the closing price is above the opening price is sometimes called a bullish candle. A general uptrend in a price is a bullish market.