Tayribeiro wrote:
Like when a person true intentions is behind something they said, but we understand what they said literally, not what they meant by using other words...
Essentially this. What the person means is not completely written or spoken, and reading 'between the lines' is understanding what was not said or written.
'Between the lines' was originally only used in reference to literary works as spoken of already, but is sometimes used in regular day to day speech.
If someone were to say, "Can't you read between the lines?" They might mean that they felt that what they said should at that point already be understood, or even that their actions were meant to convey the understanding.