An increase in the value of one currency in terms of another. Currencies appreciate against each other for various reasons, including capital inflows and the state of a country's current account. Typically a forex trader trades a currency pair in the hopes of currency appreciation of the base currency against the counter currency. 
Currency traders have to take into account appreciation when making a trade, since a long-term currency option contract might see its value decline if the value of the underlying currency adjusts. Additionally, as a currency appreciates it becomes more expensive to buy that country's exports. This can cause a contraction in the economy, which can further impact the value of the currency.