Conformity occurs when people adopt behavior and opinions to outwardly match those of a group. Conformity occurs because of the informational influence, which is the desire to be correct and to understand the right way to act in a given situation, and the normative influence, which is the desire to be liked and accepted by others.
Compliance is a behavior change that results from direct or indirect request.
Obedience occurs when people follow a direct command. A famous experiment conducted by Stanley Milgram showed the surprising lengths to which people will obey.