"And my inmost being will rejoice when your lips speak what is right"
This is the Hebrew word kilya, which means kidneys. It is translated as soul, inmost being, heart, mind. The Hebrew culture was very familiar with the kidneys because of the sacrificial system. The kidneys and the fat that surrounds them were strictly forbidden to be eaten but belonged to God. The kidneys were figuratively associated with the deepest regions of the personality and soul, seemingly because the kidneys were the deepest or last organs one came to when dissecting an animal. The worship of the wicked is called superficial; far from their kidneys. Jeremiah 12:2
In this proverb, when one's offspring begins to live wisely, it causes a deep joy in very core of your being. Few things are as satisfying.
This is the Hebrew word alaz, which means exult or rejoice. It is the natural upwelling from the soul of great positive feelings and emotions. It often accompanies singing and shouting.
There are few things that will bring deeper joy to the heart of a parent than a son or daughter who gets it; who begins to act and speak and think righteously. They will now make progress and glorify God, their family, and themselves.
This is the Hebrew word sapa, which means lips, speech, language. The idea is that what one says is an indicator of what the person understands. When a son or daughter embraces the crucial role of righteousness and lives out these moral boundaries that God has given us, it is a cause for incredible rejoicing. A parent must hear the child saying the right things and speaking with understanding of the correct moral and ethical boundaries before they know if the child has really embraced righteousness.
This is the Hebrew word mesar, which means uprightness or straightness. There is constantly an orientation to the divine standards of behavior in the Ten Commandments and righteousness is measured by connection to those. So when a son or daughter speaks what is right, they are acknowledging these boundaries of behavior either directly or indirectly.
Oftentimes, a son or daughter will refer to these standards obliquely, "I realized that I could not do that so I stopped and left the party." These words are music to a parent’s ear when children verbalize that God's standards have been internalized to the point that they are embraced and acted upon.
If you want to please your parents in the deepest way possible, embrace God's standards of righteousness. That will bring joy to the innermost part of their being.