Literally, it means, when a garment has just started wearing out, if we stitch it at that very time, it may last well, for some time. But on the contrary, if we avoid stitching at that time, then, after a few days, the whole dress may become a jumble of threads, you may not be able to repair it at all.
Similarly, the proverb is applicable in all other spheres of life. Suppose, one is participating in a horse race. If he does not check the hoofs of his horse at the time of starting, it is very probable, the horse may falter, and thus the man may lose the race. That one second’s care, might have won him a prize.
We should look before we leap. After the leap is taken, even ten looks may not be sufficient. A man falling ill, may be cured by ordinary medicines, if given in time. But a few days lapse may make him unfit, for any cure, even with costly drugs. A definite and timely action at that moment is very important.
A ship may sink, if the crack, once noted by the crew is not immediately plugged. So we say, a stitch in time saves us from having none stitches later on.