In mathematics, factors are the numbers that need to be multiplied together in order a get another number. Example: 2 and 3 are the factors needed to get an answer of 6 (2 x 3 = 6).
In other fields, especially those that rely heavily in sociological measures, you will hear the terms human factors and risk factors. These terms refer to are the multitude of variables that influence human behavior: intelligence, upbringing, temperament, environment, outside influences, education, and socioeconomic class, just to mention a few.
It is often possible to understand social difficulties and maladaptive behaviors when these various human factors are taken into consideration. In statistics, factor analysis is a statistical method that identifies clusters or groups of related items (called factors) on a test. These factors can range from types of questions to different aspects of personality.
For example, when you take a multiple choice test, a factor analysis can be conducted to ascertain what types of questions you did best on and worst on (maybe they did best on factual types of questions but really poorly on conceptual types of questions).