Improvising is a little bit like writing a good story. You've got to come up with characters, some sort of plot, relationships, conflict, and resolution. So, it's a little bit like writing a good story.
But, here's the rub. You're doing it collaboratively with other people--and those people have just as much say in what happens to the story as you do. That's a big difference.
The creative artist in us wants to take control, and figure out where everything is going. Solo artistic work primes us for that. But, improv is different. Thinking too far ahead actually hurts the scene because it keeps us mentally unavailable to the twists and turns our teammates are throwing our way.
So, the metaphor of an author crafting a story doesn't really work unless this improv author has multiple-personality disorder. But, that just sounds strange.
A better metaphor is this: driving down an unknown country road at night. This is more like it. The road is going somewhere, but you can't see very far ahead. In fact, if you think you know where the road is going, those sudden turns in the road will take you by surprise. But, if you commit to being in the moment, taking it as fast or as slow as you feel comfortable, and realizing you'll get somewhere eventually--it'll all work out.
Improv requires a retraining of our overly westernized minds, which have been taught to plan, set goals, and systematically reach them. This is a new way of thinking and interacting with people--being attentive to the present moment, accepting what happens, and making a contribution (which although it might be small, can affect the entire scene).