In ANOVA, factors are either fixed or random. In general, if the investigator controls the levels of a factor, the factor is fixed. The investigator gathers data for all factor levels she is interested in.
On the other hand, if the investigator randomly sampled the levels of a factor from a population, the factor is random. A random factor has many possible levels and the investigator is interested in all of them. However, she can only collect a random sample of some factor levels.
Suppose you have a factor called “operator,” and it has ten levels. If you intentionally select these ten operators and want your results to apply to just these operators, then the factor is fixed. However, if you randomly sample ten operators from a larger number of operators, and you want your results to apply to all operators, then the factor is random.
These two types of factors require different types of analyses. The conclusions that you draw from an analysis can be incorrect if you specify the type of factor incorrectly.