What is the real definition of racism?

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.