The term “factor” has different meanings in statistics that can be confusing because they conflict.  

In statistical programming languages like R, factor acts as an adjective, used synonymously with categorical – a factor variable is the same thing as a categorical variable.  These factor variables have levels, which are the same thing as categories (a factor variable does not have factors, it has categories). A special, and important, subset of categorical variables is binary (yes-no) variables, also called indicator variables.  Binary variables can reference natural 0/1 categories (buy, no-buy; cure, no-cure), or they can be dummy variables that are created out of multicategory variables, where each category gets its own dummy, indicating whether a record has that category.

In statistical modeling, factor is used synonymously with predictor variable. This is particularly the case when referring to fixed and random effects modeling – factors (variables) are either fixed factors or random factors.