Paternalism is a term that is typically used to refer to how governments treat people or, in this case, certain groups of people within their country. A paternalistic government acts as if it is the parent and the group of people is made up of children. A paternalistic government tries to care for the group of people as if they are not capable of taking care of themselves. For much of Australian history, the government has treated Aboriginal Australians in this way because they have been seen as unable to care for themselves.
This attitude can be seen as early as 1837. At that point, the government set up a system in which special laws were passed to protect aborigines and special protectors appointed to ensure that they would be given things, such as blankets and food, that they needed. Decades later, paternalistic policies became stronger and more entrenched. For example, there were laws prohibiting Aborigines from drinking alcohol. This trend was strongest in the first half of the 20th century.
Paternalism, then, refers to a time when the government of Australia deemed Aborigines to be incapable of taking care of themselves and set up systems and laws to care for them as if they were in some way incompetent.