What does racism mean?

Hi, me and my brother are having a fight about what racism means. I think that racism is all types of things. From calling someone a "Fuc'king ***'gar unprovoked to not letting someone in to a club because of their skin. But my brother says that racism is only where you stop someone from having a job or entering a shop or bar. So am I wrong in thinking that calling someone a "****'ing ni'gger" when unprovoked is racism and that racism is only where you tell someone what they can and cant do because of their race? Help me!