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

A candlestick where the closing price is below the opening price is sometimes called a bearish candle. A general downtrend in a price is a bearish market.