When a book lingers, it reminds me of why I read in the first place. I'm expanding my universe and experience of the world through reading. A book can linger because it taught me a lot of information, led to emotional insights, or caused me to view the world in a different way. A book can linger because it caused me to question my past actions or perceptions. A book can linger because it has had a profound impact on me emotionally. Whatever the reason, when a book lingers its because it's caused me to think more deeply. It causes me to reach inside myself a question why that story is sticking around in my head. Sometimes it takes me a few days or even weeks to make the connection, but once I find that "Aha!" moment of why a book is sticking around in my head, I know that I've grown.
This is what books are meant to do. They go beyond simply reading words on a page. They teach you more about the world, yourself, and how you interact with others. In that way books are active entertainment. You may look calm as you sit and read, but inside your thoughts and emotions are churning and making connections to the outside world. To me, a book that lingers has done its job.