Infer an unexpressed meaning. An early method of transmitting written coded messages was to write the secret information in invisible ink between the lines of a document. The recipient would then learn the information by reading between the lines. The phrase came to mean gaining an insight in the context of reading something into another person's words or behavior—and often both.

Fig. to infer something (from something else); to try to understand what is meant by something that is not written explicitly or openly.

to try to understand someone's real feelings or intentions from what they say or write