'Finish What You Start' can have many meanings for us as musicians, and is scalable. The trick is to identify the appropriate goal for the situation.
If, for example, you are just getting started on a new piece, this may mean learning the notes for a difficult passage well enough to get it correct nine out of ten times. Having done that, you can leave the practice room.
Or, perhaps you accompany yourself on an instrument while you sing, and you can already play the part reasonably well with the exception of a few rough spots. The goal for that practice session may be to iron out those parts so that they are neither a mystery, nor impediment to your vocal delivery in any way.
Having said that, I think that Mr. Gaiman was talking about this on a much larger scale. I believe that what he's saying is that by putting together all of these 'mini goals' into the finished piece, we get far more for our efforts. To quote an old cliché, the sum is greater than its parts.
This means knowing what the end is going to be, but also realizing that it may not be the The End. As ever growing and learning musicians it is a good sign that our concept for our music out-paces our ability to manifest it. You'll hear it performed a certain way in your head, and it remains just ever so close but out of the grasp of your fingertips.
When we 'finish' something (that may mean, perform, play in a lesson, record, etc...), we get to look at what we've done, and what we have yet to do. It's the cycle that musicians follow again and again. We need only identify the parts, and what we are calling 'the end' - for the moment.
:-)
