Essentially, racism is what most people expect it to be. It's thinking that one's own race is superior to others and that other races are either sub-human or not as gifted as one's own race. Defined by the Oxford English Dictionary racism is:
a. The theory that distinctive human characteristics and abilities are determined by race. b. = racialism.
racialism: Belief in the superiority of a particular race leading to prejudice and antagonism towards people of other races, esp. those in close proximity who may be felt as a threat to one's cultural and racial integrity or economic well-being.
racialist: a. n. A partisan of racialism; an advocate of a racial theory. b. adj. Of, pertaining to, or characterized by racialism.
This basically sums up what "racism" is. Yet there is racism and then there is white supremacy, which comes from white privilege, and comes from a society that has favored (and given rewards to) white people over people of color. Essentially, anyone can be a "racist." A Korean American father and mother could get upset at their son or daughter for a dating a Black person because they think Black people are "lazy" and "dumb" and a Black person could hate white people because they think that white people are inherently "inferior" and that the Black race is the superior race and the white race is the inferior devil race. Yet there is a marked difference between a Black person being racist and a white person being racist and enacting certain policies that affect many people of color around this country (and the world).
With the term racism, there is no power structure being implied in its use. With the term white supremacy there is a power structure being implied in its use. While a person of color can be racist it's not the same as a white person being racist and/or using his or her white privilege to gain an upper hand in society. A person of color may have racist thoughts but those thoughts are rarely enacted through the power structures of our society to effect mass change and to affect other people. The power structure in our society has been built up over time on white privilege and white supremacy and the people that have been exploited to make this country "great" were people of color. This structure is still in place and people of color are still in worse off situations than whites are (see "Living on the Other Side of the Color Line") and whites continue to benefit from a society that views white as the "norm" (white heroes in history books, whites in TV shows, whites in congress, whites as CEOs, etc.) and continue to benefit from past racist policies and from current racist and contemporary racist thought (see "Black Dolls/White Dolls," "Anti-Gang Injunctions," "Boxer Recalls Award," among other posts) as well as intentional or unintentional racist policies from the government that harm people of color but tend to not harm the white population. A person of color can be a racist, of course, but a person of color (due to the cited references above) cannot act on her or his racist views and in no way can harm whites at a mass level.
Someone who is a white supremacist (not in the classical KKK sense but in the more contemporary sense) in contrast can act on her or his racist impulses more often than not and still receives benefits from society despite being racist. Someone who is white and who holds the views that most welfare cases are "lazy Black mothers" (which actually isn't the case, from what I've been told) holds more sway (through lobbyists) than do people of color arguing that welfare shouldn't be changed since it will adversely effect people of color. This was the case under Clinton who changed the welfare laws during the 1990s. Also, white privilege holds sway over vast swaths of American life and affects people of all ethnic groups. Whites, most of the time, do not see their own privilege and enact policies, or lobby for policies, that would benefit them while in turn disenfranchising many people of color (all though they would do this under the guise of being "color blind" or that they believe all races should be "treated equally"). We see in the power structures of America that most of the people at the top (except for a few token exceptions) are white males, from the executive, to the judicial, to the congress, to the CEOs of Fortune 500 companies, to many mid-level and high-level bureaucrats in major cities. These white people at top tend to hold many views that mainstream white Americans hold and in turn these views effect the way they govern and interact with other whites and other people of color. And this doesn't just include those in bureaucratic power put in everyday life as well and in everyday interactions that white people have and that people of color have. A white person would be hard pressed to remember the last time he or she had security follow them around a department store or having a cop asking them if they were lost because they were in such a "nice neighborhood" while a Black person could probably draw upon experiences from just the past month.
Another point on power structures and the difference between racism and white supremacy (which is not the same as Black or Brown power, etc.) is that racism also tends to imply that all races are "equal" and that all races can be "equally racist." Yet the reality of America is that not all races are equal. One could argue under a multicultural guise that whites need their own "European History Month," or day, etc. yet this ignores the fact that not all races are equal. The white race was essentially built up on privilege and didn't come from an ethnic group. There is no such thing as the white ethnicity (as suppose to the Han ethnicity or the Mein ethnicity or the Lgbo Nigerian ethnicity), "whiteness" was defined over the generations and was solely defined from privilege and exploitation. Not all racism is equal because not all racism affects people on a wide scale, but other types of racism do affect people on a wide scale. This is where the term white privilege and white supremacy come in. It's not enough to use the term racism, especially against people of color, since it is white supremacy that is prevalent in American society and it is white supremacy that effects the most changes in society and gives whites the most benefits and people of color the least benefits. Racism implies all types of racial bigotry are equal when in reality there is one type of racism that is above all else, that is white racism against people of color, white supremacy; and therefore using the term racism as a blanket statement for all racism in general, whether it be Black racism, white racism, Asian racism, etc. is not adequate enough and not accurate enough.