For functions in multi-dimensional space, if the Laplacian of such function is zero everywhere, that means it is harmonic. The laplacian is sort of the second derivative for multivariate calculus.

Suppose that the laplacian of a function is zero everywhere. This means it is harmonic. This concept arises all the time in physics, capturing a notion of stability, whenever a point in space is influenced by its neighbors.

This means essentialy that the second derivative, being zero everywhere, the function this laplacian represents will have a stable pattern, with its first derivative never changing, the stability around a given point.

It indicates how much of a minimum or maximum a given point is: how stable or unstable it is.