A negative correlation coefficient means that, for any two variables X and Y, an increase in X is associated with a decrease in Y. A negative correlation demonstrates a connection between two variables in the same way a positive correlation coefficient does, and the relative strengths are the same. In other words, a correlation coefficient of 0.85 shows the same strength as a correlation coefficient of -0.85.
Correlation coefficients are always values between -1 and 1, where -1 shows a perfect, linear negative correlation, and 1 shows a perfect, linear positive correlation. A correlation coefficient of zero, or very close to zero, shows no meaningful relationship between variables. In reality, these numbers are rarely seen, as there are very few perfectly linear relationships. Instead, numbers approaching these values are used to demonstrate strength of a relationship; for example, 0.92 or -0.97 would show, respectively, a very strong positive and negative correlation. As with all statistics that demonstrate correlation, this does not prove causation.
It is easiest to grasp the concept of negative correlations through examples. A simple one would be measuring the amount of snowfall and the temperature. As the temperature increases, the amount of snowfall decreases; this shows a negative correlation and would, by extension, have a negative correlation coefficient. A positive correlation coefficient would be the relationship between temperature and ice cream sales; as temperature increases, so do ice cream sales. This relationship would have a positive correlation coefficient. A relationship with a correlation coefficient of zero, or very close to zero, would be temperature and fast food sales (or at least, this is what we would assume).