This proverb advises us to be prudent. Timely action often prevents some great loss or harm that could occur in the future. If there is a small rent in your garment, you would be wise to put in some timely stitches. If you let it be and put off the repair of the garment, the rent will turn into a larger hole and finally, the garment will become absolutely useless and impossible to wear. If a crack in the embankment of a river is not repaired in time, the water will keep on seeping through, the crack will widen and might even result in large-scale flooding.
It is the same with all situations affecting humans and their actions.
As soon as one observes that something is wrong. one should take immediate steps to rectify the situation. If one sits by and does nothing, the situation will worsen and then might turn so bad that massive efforts will have to be taken in order to put the situation right.
As Benjamin Franklin said, "Never leave till tomorrow what you can do today." The simple problem that you have unsolved today will develop into a situation that might require enormous efforts to deal with tomorrow. Tackle the problem as soon as you see it. It will save you plenty of time, money, misery and heartburn in the future.