What does Proverbs 25:3 mean?

This verse compares three things to explain why the decisions of kings and other rulers may not be understood by others. The overall point is that the thought process of those in power is difficult to assess. Subjects, citizens, employees, or others who don't have access to the same information may not understand why certain decisions are made. This is not to suggest that rulers should be blindly trusted merely because their mindset is obscure (Acts 5:29). Rather, the teaching is that those in higher authority tend to be more self-contained in their thoughts; their thought process is naturally less transparent.

The first comparison is to the height of "the heavens," using a Hebrew word with multiple meanings. "Heavens" can refer to the visible sky, the region beyond the sky, or to the dwelling place of God. Here, it's probably a reference to the visible sky, as the second comparison is to the depth of solid ground. Modern science suggests the "height" of the universe beyond earth stretches for billions of light-years. That's almost certainly not what Solomon had in mind. Despite myths of popular culture, scholars from the ancient world held some understanding that the planet was spherical, even attempting to calculate its size. In both cases, Solomon is not referring to some exact number, but rather to the obviously profound size of those two distances.

Comparisons of the king's heart to these enormous heights are hyperbole: deliberate exaggeration for effect. Because of that technique, the meaning is made clear. A king, ruler, or other person in authority typically has knowledge unavailable to others. As with all proverbs, this is a general case statement, not an absolute rule. Even kings can be ignorant, uninformed, or oblivious. The following verses note how important it is for those leaders to seek good counsel (Proverbs 25:4–5). In most cases, however, those in authority have access to information which subjects, citizens, and employees typically cannot see.