What is it called when an author makes reference to something without to explicitly stating it?
This literary device is called allusion.
Allusion is an author's direct or inferred reference to a person place or thing. It can be a historical manuscript, a famous speech, a movie, a play, a novel, a well-known event, and much more.
The purpose of this device is to engage the reader, to communicate an idea subtly and concisely, to suggest the cultural meaning of something, and to set the tone of the piece.