Actual classification of the term racism is quite complex.
In its most fundamental form, which is a perfectly valid definition for it, racism is:
Discrimination or prejudice based on race
Another definition of racism is :
The belief that race accounts for differences in human character or ability and that a particular race is superior to others
Typically this will be the belief that Whites are superior and any legislation based on this belief is also racist, such as the apartheid system in South Africa and the automatic acceptance for immigration into Israel for Jews and 3rd generation descendants of Jews.
Prejudice is a very important factor when looking at what constitutes racist behaviour.
Prejudice can be defined as:
An adverse judgment or opinion formed beforehand or without knowledge or examination of the facts
or
A preconceived preference or idea
or many other things. There are many definitions for prejudice because its usage can be wide and varied.
the most important thing about prejudice is that it deals with pre-judgements, that is, judgements without the specific facts about that which is being judged. In the case of a person (which is most relevant when discussing racism), it refers to the individual. Whilst this is quite evident, I shall explain further - from the definition of prejudice as: "An adverse judgment or opinion formed beforehand or without knowledge or examination of the facts", it can be seen that to judge a thing without that judgement being prejudicial, one must be in possession of some facts about that thing (subject). Should the thing (subject) be a person, then there are degrees to which that person can be fairly prejudged without it being prejudicial based upon knowledge of
universal characteristic traits (judgements based upon human physiology for example) any form of personality trait (since personalities are not universal and cannot be fairly and logically judged based on anything other than interaction with the indivdual or second hand information about that individual) judged upon a stereotype, whether or not it is justified, whether or not it is correct, whether or not it is based upon personal experience of similar things, is prejudicial.
Any judgements not based upon actual knowledge of that individual can be considered to be prejudicial. If those prejudices are based upon race, then they are racist - according to the definition of racism as "Discrimination or prejudice based on race".