Skewness measures (or refers to) a degree of asymmetry in the distribution of a variable.
Skewness usually refers to standardized third-order measure of asymmetry in a distribution: that is, a centralized third moment divided by the cube of a standard deviation. Histograms of positively skewed distributions will typically have a long "tail" of relatively high values; those of negatively skewed distributions will usually have a long tail of relatively low values.
More generally, and much more qualitatively, "skew" is sometimes used synonymously with "asymmetric". Note, however, that a distribution can be asymmetric but have zero skewness.
The usual measure of skewness for a dataset $x_i$ ($i=1,2,\ldots,n$) with mean $\bar{x}$ is given by:
$$\frac{ \frac{1}{n} \sum_{i = 1}^{n}{\left(x_i - \bar{x}\right)^3}}{\left( \frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2 \right)^{\frac{3}{2}}}$$
