A fixed effects model is a statistical model which accounts for individual differences in the data which cannot be measured by treating them as non-random, or “fixed” at the individual level.
As an example, let’s say we wanted to study if drinking coffee makes people are more likely to cross the street despite a red light. Our outcome variable of interest is how often each subject crosses a street despite a red light on a walk with 10 red traffic lights. The explanatory variable we manipulate for each participants is if they had a cup of coffee before the experiment or a glass of water (our control condition), and we would use this variable to try to explain ignoring red lights.
However, there are several other influences on ignoring red lights which we have not accounted for. Next to random and systematic error, we have also not accounted for individual characteristics of the person such as their previous experience with ignoring red lights. For instance, have the participants received a fine for this offense? If so, they might be less likely to walk across a red light in our experiment.
Using a fixed effects model makes it possible to account for these types of characteristics that rest within each individual participant. This, in turn, gives us a better estimate of the relationship between coffee drinking and crossing red lights, cleaned from other individual-level influences.