Skewness measures the lack of symmetry of a probability distribution. A curve is said to be skewed to the right (or positively skewed) if it tails off toward the high end of the scale (right tail longer than the left). A curve is skewed to the left (or negatively skewed) if it tails off toward the low end of the scale.
Skewness of the distributions whose density is symmetrical around the mean is zero. The reverse is not true - there are asymmetrical distributions with zero skewness.
Skewness characterizes the shape of a distribution - that is, its value does not depend on an arbitrary change of the scale and location of the distribution. For example, skewness of a sample (or population) of temperature values in Fahrenheit will not change if you transform the values to Celsius (the mean and the variance will, however, change).
See also: Kurtosis