A numeric variable is continuous if the observations may take any value within an interval. Variables such as height, weight and temperature are continuous.
In descriptive statistics the distinction between discrete and continuous variables is not very important. The same summary measures, like mean, median and standard deviation can be used.
There is often a bigger difference once inferential methods are used in the analysis. The model that is assumed to generate a discrete variable is different to models that are appropriate for a continuous variable. Hence different parameters are estimated and used. (See also discrete variable, mixed variable.)