Variability refers to how widely the value of data points making up a given data set are spread out. A small variability implies all the data points in the set have a value that is nearly equal while the variability is very large if data points have a value that differs to a large extent.
The range is the difference between the smallest and the largest values in a given set.
Standard deviation is calculated in a more complex way. To determine the standard deviation, first the average of all the values in the set is estimated. Then the difference of each of the values from the average is calculated and it is squared. The square root of the sum of the squared values is the standard deviation.