Variance ratio or co-efficient of dispersion is defined as the ratio of variance to mean. It is defined only for those models, where the mean is non zero. It is frequently used with exponential and Poisson distribution for count data etc.
In the world of statistics, variance ratio is used to measure how dispersed or clustered set of events are, in a given interval of time or space.
IF variance ration = 0, the underlying distribution will be a constant random variable
If 0< variance ration <1, underlying distribution could be binomial
If variance ratio = 1, underlying distribution is Poisson
If variance ratio >1, over-dispersed negative binomial distribution.
For example, variance ratio of 1 indicates Poisson distribution. Now if we want to detect, whether the distribution of earthquakes in a given region is poissonian in nature or some other factors are involved, we try to collect the data set and find the variance ratio for the same. If VR = 1, it indicates Poisson distribution.