Bias is the conscious or unconscious favoring of one person, group, or thing over another that prevents a person from acting impartially or fairly. Bias is different than having a preference, like in dating. It involves how we react to the favoritism even it's on a subconscious level. People can have biases over pretty much anything, but common biases include gender, race, culture, age, disability, sexuality, and weight. See below for the different kinds of biases.
Explicit bias is our conscious beliefs that we are aware of and openly express. Hate groups and openly prejudice people show explicit bias. Because of this visibility, explicit bias is the type of bias that most people think of.
The "advantage" of this visibility and awareness is that it makes it easier to overcome than other types of biases.
Implicit bias, or unconscious bias, is our unconscious beliefs. These are the biases that we are unaware of and may expressed unintentionally or nonverbally through body language. Implicit bias can also cause us to react in ways that we consciously believe are wrong. For example you may believe that racism or sexism is wrong, but still unintentionally act negative towards certain people. Having a black/gay/disabled/etc friend, doesn't mean you don't have biases against that group - you just may not be aware of it.
Because implicit bias happens "silently," it is much harder to spot and to overcome than explicit bias. Making it even harder to overcome are confirmation and negative biases.
Positive bias is the positive thoughts or beliefs about others based on their race, gender, sexuality, religion, and more. Like implicit bias, this can cause problems in how equal we treat people. For example, some people have a positive bias that all college students are geniuses and because of this, won't give college students the same level of directions or help that they give other people. They assume you already know what to do - even though completing a task has nothing to do with intelligence. Have you ever ask for help and had the other person seem surprised you asked? That's probably positive bias in effect.