Autonomy means being able to rule without having to obey some other higher authority. Autonomy is something that philosophers often talk about. The idea occurs in moral, political, and bioethical philosophy. It means that someone is able to make a sensible decision without being forced to do so by someone else. They are able to make a "free" decision.
In moral and political philosophy, autonomy is often used when discussing whether someone has a moral responsibility for what he does. One of best known philosophical theories of autonomy was developed by Kant. In medicine, doctors have to respect the autonomy of the patient, i.e. the patient has been given good information about their illness, they should be able to decide whether they want treatment. The doctor cannot force it on them.
In politics, autonomy means self-determination that people can govern themselves instead of being ruled by someone else.