The One-Sample Kolmogorov-Smirnov Test procedure compares the observed cumulative distribution function (CDF) for a variable with a specified theoretical distribution, which may be normal, uniform, Poisson, or exponential.
The Kolmogorov-Smirnov Z is computed from the largest difference (in absolute value) between the observed and theoretical cumulative distribution functions. This goodness-of-fit test tests whether the observations could reasonably have come from the specified distribution. For example, many parametric tests require normally distributed variables.
The one-sample Kolmogorov-Smirnov test can be used to test that a variable (for example, income) is normally distributed.
If the p value is significant for example, less than 0.05 then data cannot be considered as normally distributed (and parametric tests cannot be used), since the null hypothesis is observed CDF is not different from normal distribution.
The Kolmogorov-Smirnov test is often shortened to the K-S test. It is also referred to as the 'vodka test' after Smirnov brand vodka.
For the comparison with Kolmogorov-Smirnov Two Sample Test, please refer to Kolmogorov-Smirnov Two Sample Test.