This week we're starting off with a lesson that could be illustrated by our throwing a pebble into a pond . . . it can be a very tiny pebble, but we will still see ripples spreading out from the place the stone hit the water, right? I imagine all of us have done that; when you were small you may have been with an adult and skipped stones on a pond, or dropped a rock or stick over the side of a wooden pier. Even a tiny pebble dropped into a puddle will have the same effect --- those ripples keep growing and growing.
Pro 19:25 Smite a scorner, and the simple will beware: and reprove one that hath understanding, and he will understand knowledge.
Here is where the pebble hits the pond -- the punishment of scorners, those who despise wisdom and laugh at instruction, is a means of good to others. The reproof of wise men will be a means of good to themselves and to others. Some people have hardened their hearts and will not listen to reproof or instruction, though it is for their benefit. Even if they themselves will not respond to the chastisement, others may see their plight and "clean up their act" before it is too late. In Deuteronomy, God (through Moses) was giving the law to the children of Israel, and telling them the penalty for false witnesses in a trial, saying, "And those which remain shall hear, and fear, and shall henceforth commit no more any such evil among you." (Deu 19:20)
In other words, the punishment was to be a warning to others; as the ripples spread out, they would see and not follow the same path.
The second part of the verse is this: the reproof of wise men will always be a means of good to themselves and to others. Solomon must have felt it was pretty obvious -- you don't need to smite the wise man; just a "word to the wise" should be sufficient. And it usually is. Once the wise man (or woman) has been told, he or she will take the reproof to heart, and listen, and learn, and increase in understanding and wisdom. There could be two kinds of ripples here: others can see how the wise person accepts and profits by reproof, and also the wise person can be a gracious instructor of others.