Racism is such a challenging concept to define in one sentence. It is often simplified to discrimination against a person or group of people based on their race. Many still think, and certainly the law in many countries still defends this notion, that racism only matters when it is intentional. This is very limiting.
It is often forgotten that racism does not only disadvantage some people based on race, it also privileges people based on race. Some believe that racism cannot be limited to racial prejudice; racism takes place when a group of people with power are able to act on their racial prejudice in a harmful way.
It can be helpful to break it down into three categories (by no means the only possible categories):
Interpersonal racism – prejudices and discriminatory behaviours where one group makes assumptions about the abilities, motives, and intents of other groups based on race. This set of prejudices leads to cruel intentional or unintentional actions towards other groups.
Internalised racism – when members of stigmatised groups are bombarded with negative messages about their own abilities and intrinsic worth, they may internalise those negative messages. It holds people back from achieving their fullest potential.
Institutional racism – when organisations, businesses, or institutions like schools and police departments discriminate, either deliberately or indirectly, against certain groups of people to limit their rights. The Stephen Lawrence Inquiry defined it as "The collective failure of an organisation to provide an appropriate and professional service to people because of their colour, culture, or ethnic origin. It can be seen or detected in processes, attitudes and behaviour which amount to discrimination through unwitting prejudice, ignorance, thoughtlessness and racist stereotyping which disadvantage minority ethnic people" (Macpherson, 1999).
Dismantlingracism.org also provides an interesting breakdown of racism that links it more simply to privilege and social oppression:
Racism = race prejudice + social and institutional power
Racism = a system of advantage based on race
Racism = a system of oppression based on race
Racism = a white supremacy system
Racism is different from racial prejudice, hatred, or discrimination. Racism involves one group having the power to carry out systematic discrimination through the institutional policies and practices of the society and by shaping the cultural beliefs and values that support those racist policies and practices.