What is the physical significance of the laplacian operator? The laplacian operator is the divergence of the gradient. I understand the intuitive meanings of both. The gradient when dotted against a unit vector gives the rate of change in that direction. The divergence is the flow in or out of an infinitesimal sphere surrounding a point. But I can't quite figure out what they mean when used together. I was wondering if there was a simple way of describing it visually.