What does the proverb 'a stitch in time saves nine' mean?

Literally, it means that a single stitch (to fix a tear in a garment) will avoid having to make many more (nine) to fix a larger tear that it might cause.

Figuratively, a little work today (one stitch) can save a lot of work later on (the nine stitches). For example, fixing a tile on the roof can stop the wind and water from getting in and causing a lot of damage to ceilings and so on. Or putting a little oil in the car engine can avoid a ruined engine, a ruined trip and an expensive repair.

Think of a small rip in a stitched seam. If one were to restitch the hole in the seam while it is small, it won't take nearly as much effort as when the hole has time to work itself into a larger hole.

It is often best to fix problems soon after they are discovered, so that they don't grow into larger problems that will require a lot more effort to fix.
Fix in now, it will only get worse later and then be more difficult to repair