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.
A Stitch in Time Saves Nine
A stitch in time saves nine and a malady which is curable today and within the control of the physician my become incurable tomorrow and get out of the control of the physician.
As they say evil should be mapped in the bad. At any rate, it should not be allowed to gain a firm foot hold. Once it gets a foothold, it becomes a very difficult to eliminate it. It is easier to prevent a boy from smoking if he started smoking only a few days back that if he has been smoking for the last year.
As a student should always keep in mind to postpone doing the work which he can do today to tomorrow. When work piles on work the he begins feeling nervous and diffident with the result that my times the fails in the examination. A stitch is time does save nine.
A stitch in time saves nine is a plea for immediate action and promptness and agility in life. Postponement of action is often injurious. We should clutch opportunities. Once we let them go unnoticed, it becomes difficult to call them back. John Ruskin did not let opportunities skip away, he always tried to stitch in time. He realized fully the importance of today and as Date Carriage tells us in his wonderful book: ‘How to stop worrying and start living’, he had on his desk a simple piece of stone on which was carved one word – Today.
A stitch in time as saves one from a lot of mental worry and brooding. One who does not work on time, keeps on worrying and brooding over the work tell it is not done.
Once should not allow things to deteriorate. A cold, if not treated at the right time, may develop to pneumonia. Timely stop or action is always safe and sound. Delays are dangerous.