In statistics correlation refers to relationship between two variables. When the value of one variable varies closely with variation in another, the two variables are said to be correlated. For example if the sale of umbrellas in a town during the rainy season is found to vary with the the amount of rainfall during the season than we can say that the sale of umbrella and amount of rainfall are correlated.
Correlation coefficient is a statistical measure of how close this relationship is. A correlation coefficient of 1 indicates a perfect or total dependence between two variables. For example, if we were to calculate the correlation coefficient between temperature in Fahrenheit and Celsius it will be equal to 1. A correlation coefficient of -1 means the variables are inversely correlated. For example, the volume of a given weight of different substances is inversely proportional to their densities therefore the correlation coefficient between these two will be -1. A correlation coefficient of 0, implies no correlation. But in reality this only implies that there is no linear relationships. For example some graphs of two related variable have shapes lie 'U' or 'inverted U'. In these cases the relationship exists but is not linear. Therefore correlation coefficient is likely to be close to 0.