Bias is a tendency to lean in a certain direction, often to the detriment of an open mind. Those who are biased tend to believe what they want to believe, refusing to take into consideration the opinions of others. To truly be biased, it means you're lacking a neutral viewpoint. Sprouting from cultural contexts, biases tend to take root within an ethnic group, social class, or religion.
Bias, prejudice, and discrimination all live under the same roof. Bias is an inclination toward one way of thinking, often based on how you were raised.
For example, in one of the most high-profile trials of the 20th century O.J. Simpson was acquitted of murder, but many people will remain biased toward him and treat him like a convicted killer anyway.
Prejudice is a feeling toward a person based solely on their affiliation with a group. It often casts an unfavorable light on someone simply because they're a member of some family, church, or organization.
For example, millions of people around the world consider Tom Cruise to be a very talented actor. He's also labeled as one of Hollywood's nicest guys, purportedly treating his cast and crew with the utmost kindness and respect. However, his affiliation with Scientology prompts all kinds of negative press, causing some people to feel prejudice toward him.
Discrimination comes into play when one starts acting upon an inherent prejudice they possess.
For example, during the time of slavery, men and women held prejudices against African Americans and, in turn, discriminated them through slavery, segregation, and other heinous acts.