Meditation practitioners refer to the inner "story" that most of us have going on in our minds so much of the time. We tend to live in our minds, with our thoughts narrating our experiences: "I like this." "I don't like that." "I want more of this, less of that."
We can identify so much with our inner stories that we miss out on new experiences and opportunities. A meditation practice helps us sit in awareness of our stories, yet without overly identifying with them. During a meditation session we can invite our stories in -- as Thich Nhat Hanh suggests, we can tell ourselves "Dear One, I am here for you" and listen compassionately and non-judgmentally to our stories -- but then we can also train our minds to let the stories go. This letting-go is often called "dropping the storyline," or "nonidentification with the story."
Dropping our storyline doesn't mean we don't make changes when we need to; it does mean that we become less preoccupied with or controlled by ruminative thoughts or negative emotions that may not be useful to us...and more clear about when and how to take action.
Paradoxically, it all starts with a welcoming awareness and compassionate acceptance. We invite the stories in, without trying to solve anything -- "Have a seat and tell me all about it. I'm here for you." And then we practice letting them go.