Factorial experiment is a designed process that helps understand the impact of two or more input variable on the output of a process. By being able to estimate the impact of the input parameter on the output with the help of comparatively lesser number of observation helps in the optimization of the process. The effect of varying the level of the input variable on the output is considered.
For Example if we want to study the impact of using a fertilizer and irrigation on the yield. Say irrigation can be low or high and even fertilizer used can be less or more. Now four sets of input exist. The effect of each set of input on the output is referred to as the main effect of the factor. Each set of the input variable is referred to as a factor. A given can have large number of levels.
However for ease usually only two levels are taken for a factor. In case of more than two some levels are omitted for ease. In the above example irrigation and fertilizers are the factors. High or low refers to the level. For an experiment with n number of factors and each having 2 levels the number of experimental conditions are 2^n. in the above case it is 2^2=4.