In trading, correlation is a measurement of the relationship between two assets.
A positive correlation suggests that Security B will move in the same direction as Security A.
For example, the http://www.babypips.com/school/eurjpy-your-very-own-barometer_of_risk.html German stock market (DAX) and EUR/JPY moved in the same direction from 2004 to 2010. That is, EUR/JPY rose when DAX performed well and plummeted when the stock market dropped.
A negative correlation suggests that Security B will move in the opposite direction of Security A.
An example is the correlation between http://www.babypips.com/school/using-the-usdx-for-forex.html EUR/USD and the dollar index (USDX]. A strong dollar would usually lift USDX, but it will also boost the dollar against the euro, resulting in a downward price action for EUR/USD.