I am not sure what you mean by the "real" definition, but here is how I would define it.
I would say that racism is the idea that people of one race or many races are inferior to some other race or races. This definition implies a couple of things:
First, it implies that there is such a thing as race. Scientists tell us that there is really no such thing as race -- that there are as many differences between people we call "black" as between "blacks" and "whites." So in order to have racism, you first have to believe that there is a difference between one kind of person (we'll call that a race" and another.
Second, you have to believe that there are traits that are inherent to these races. You have to believe that some race is always inferior. You believe that they are just naturally inferior -- not just that they're less educated, or unlucky, or whatever.
So racism is this idea that there are races and some of them are inferior to others.