Prejudice means preconceived opinion that is not based on reason or actual experience. The word comes from the Latin "pre" (before) and "judge". People may prejudge any question, but the word is often used for an opinion about a person or group of people. English understanding of the Latin has changed in past centuries. In old English the word "prejudice" denotes the use of "good judgment" before an event, e.g., "I decided (showed prejudice) not to run with the bulls because I could have been hurt".
The word "prejudice" is often used when people dislike another group of people that are different from them. They may decide they do not like them because of their skin color (this is "racial prejudice"), religion (religious prejudice) or nationality. Such prejudices can lead to discrimination, hatred or even war.
Judges in a court of law should not be prejudiced when deciding whether someone is guilty. They should have an "open mind" so that they can make a fair decision (this is also known as not having a bias; most judges in a court of law have sworn to be unbiased when deciding a penalty). For example, if that person is the judge's friend then the judge would be prejudiced because he (or she) would not want his (or her) friend to get into trouble. In many other situations it is important not to be prejudiced, such as serving as an adjudicator in a competition or a juror in a trial.
Modern people sometimes use "prejudice" to mean "bigotry." This leaves them with two words for one thing, and none for the other.