Many of the methods used in Statistical Process Control rely on the data conforming to a normal distribution. The central limits theorem is important because it states that even if the process itself does not conform to a normal distribution the means of samples taken from the process will tend to be normal, the larger the sample the greater the tendency. Thus we can analyze sample (subgroup) means in a way that would not be valid if applied to individual data values.
Suppose you:
 take a large number of samples from a population that does not conform to a normal distribution
 calculate the mean each of those samples
 find the shape of the population distribution formed by these sample means
You will find that the distribution of the sample means will resemble a normal distribution. The larger the the number of items in each sample, the better the approximation.
