If you take the time to do something right the first time, then it will stay done.  In other words, you can do the stich right the first time or redo it again and again nine more times.  Wouldn't you rather do it right the first time then?

This old adage, "A stitch in time saves nine" is similar in meaning to another one:  "An ounce of prevention is worth a pound of cure."  The concept of both of these involves making productive use of one's time, doing things conscientiously and well the first time.

With this theme in mind, a narrative about a character who is not diligent in his studies or at his work, but who takes the quick, easy and flashy way that will get him attention and envy from his associates may serve you well.  For instance, you may be inclined to write about a student who quickly puts together a science project for a fair and draws the attention of the judges, but when he begins to demonstrate his experiment, the project collapses.  Then, the judges move to another student, who has always been second to the first at school, but now has his/her day of glory for his/her diligence and conscientiousness.   Or, you can write about someone in an office who promotes his/her ideas and moves ahead of the others until he/she has omitted an important subject or page from his/her report and must work long into the night correcting the error while someone else takes an effective report to the boss that evening and wins the assignment.

This proverb is a metaphor that draws from the image of sewing, or more likely, counted cross stitch.  In fact, it was probably a very common saying to stitch into samplers.  Essentially it means that if you take your time to work "in time" or slowly but steadily, you will likely avoid bigger problems in the future.

I assume from your question that this is a creative writing assignment.  If I were you, I might try to think of a true story (personal is even better) of a time when rushing through something at the beginning caused more problems and took far more time to resolve than had you worked slowly and carefully from the very beginning.

"A stitch in time saves nine" is a saying that often goes hand-in-hand with the wisdom that comes from experience.  I can think of many people's experience in college with putting off studying for an exam or major projects until the last minute.  In the end, it would have been far more worth it to spend more time on the front end, when they considered how much longer they spent digging themselves out of a failed grade or retaking an entire course.