I have the feeling that when most people hear the word "improvise," they think of something that is the opposite of planning, as in "I didn't plan for it, I just improvised." In other words, improvising is the same as winging it. Following this logic, improvisation doesn't require work or planning; in many ways it is the opposite.

I think of improvising differently, perhaps because I have been playing music since I was a young child. As a musician, improvisation is an activity that takes skill and practice. To be good at improvisation requires an understanding of music theory (intuitive and cognitive), a good ear, and enough chops (skill on the instrument) to create the appropriate musical sounds on the fly. Each musician develops improvisation skills a bit differently. For me, it comes from time spent mastering various kinds of scales, rhythms and chord progressions (building on the blocks of melody, harmony and rhythm)--that it what I call "practice." It is very similar to drills performed by athletes. And it is different than learning and playing songs--I consider that "rehearsal." Important and necessary, but it doesn't develop me as a musician in the same way that practice does.
Disciplined Practice & Preparation: A Key to Improvisation
I am able to improvise as a musician because I prepare and practice. The musicality of my improvisation is a result of my understanding of music, a trained ear, and enough skill/muscle memory with my chosen instruments to create something interesting in the moment. When I do not put time and effort into practice, I quickly lose my creative edge and I have a harder time playing something interesting when I improvise.

I find the same thing is true when I am running a gaming session. I am able to improvise best when I am well-prepared and I have put in the necessary time to plan. I am able to draw upon the complexities of the world I am creating and the vast resources of gaming community to respond creatively to player activities during a session. That to me is improvising. I am not smart enough to run a good session by winging it any more than I can create an interesting guitar solo without practice.

I relearn this every time I run a session without preparation, as I have done the last few weeks in our Montporte Campaign. I have been run ragged by work and have nothing left in the tank to devote to preparation and planning. The less I prepare and plan and am forced to improvise, the less I am able to improvise effectively. I just end up drawing blank after blank. I notice myself struggling; it is probably not apparent to the players in any given session. However, there is a cumulative impact on not preparing that makes the sessions less interesting and challenging for players.

Like any analogy, there is a point where the analogy between playing an RPG and playing music breaks down. However, because both music and RPGs have elements of performance art to them and they are also typically group activities, there are a number of analogies that can be drawn. Improvisation is one such analogy.