Factors are predictor variables (also called independent variables) which you choose to systematically vary during an experiment to determine their effect on the response (dependent) variable.
For example, you want to inspect the surface finish of metal parts coming from several machines and measured by several operators. Both 'Machine' and 'Operators' are factors in this experiment. 'Machine' and 'Operators' can be crossed or nested factors, depending on how experimenters collect the data.
Two factors are crossed when each level of one factor occurs in combination with each level of the other factor.
Two factors are nested when the levels of one factor are similar but not identical, and each occurs in combination with different levels of another factor.