Explain the relationship between racism and privilege.

Racism states that one or more designated race is inherently inferior to other races. Because individuals of these races are deemed inferior, they are perceived as unfit for roles of leadership or authority within a culture. They are often characterized as childlike and in need of the guidance and protection of the superior race—or, like the Jews in Nazi Germany, they may be seen as inherently evil or in need of severe discipline and/or eradication.
Because one (or more) race is considered unfit for leadership and perpetually childlike, it follows that it is only right that the bulk of the privileges adhere to the so-called superior race. After all, a childlike, backward race can't handle money or power, doesn't know how to be in charge, and can't benefit from more than a rudimentary education.
Once one race is able to amass power and create a convincing discourse that depicts another race as inferior, it follows that the inferior race should not share the privileges of the superior race. It seems "natural" that society's benefits should flow to those deemed most deserving of them.
It should be kept in mind that "race" is almost entirely a social construct. For example, a person even 7/8ths white and 1/8th black in the antebellum south was deemed black and, therefore, could be enslaved. Racism had nothing to do with actual inferiority and everything to do with manufactured inferiority that protected white privilege, which, many argue, continues to be the case today.

Privilege is a certain sense of immunity, right, or freedom granted to a person, and this plays a major role in society. In an egalitarian society, privilege does not really exist because all members of the group are treated equally. In a stratified society, privilege is limited to a certain portion of society or at least made more difficult for some to attain. Race is an unfortunately common factor in "justifying" social stratification, especially in cultures where there is a history of colonialism or slavery.
Racism is the devaluation and discrimination of people of a particular "racial" group, typically distinguished by physical characteristics like skin, hair, and eye color. While organizing people into certain groups based on shared physical characteristics is not an act of violence on its own, the conflation of arbitrary values and characteristics and the devaluation or preference for certain physical traits is. In societies where race is a factor in stratification or access to privilege, these physical characteristics can enable or hinder a person's agency in life. 
The allocation of privilege based on race relies on false justification through the conflation of arbitrary values with visible characteristics. To avoid using real racial myths, imagine you live in a society where people have wildly colored hair. Red, blue, purple, orange, green, any color you can think of. Now imagine it's really valuable in this society to go to flight school and become a pilot, but people with green hair are often denied entry into flight school based on the "justification" that people with green hair are naturally bad pilots. I understand this is a pretty ridiculous sounding example, but it demonstrates just how ridiculous it is to conflate arbitrary characteristics like job performance with someone's physical traits.
https://dictionary.cambridge.org/dictionary/english/privilege