What does it mean to read between the lines?

Read between the lines.

If we hear of a father who thinks so much about his children, who has created so many attractions and diversions and exercises for their minds, so that they might never be dull and never seek another companion, we would say at once—

What a wonderful thing to have a father's love like that! 

With us, all this is applicable exactly? We all are in that happy position of having a Father who thinks that nothing could be too beautiful, too wonderful for His children.