When you drop out, you stop taking part in something. Your parents might not approve of your plan to drop out of high school and join the circus.
People drop out of all kinds of things, from college to sporting events to political races: "He'll probably drop out of the presidential race after the primary." If you drop out of school, people might call you a dropout. As a verb, drop out has been used since the 16th century to mean "withdraw," while the sense of "stop going to school before graduating" started in the early 20th century.