This tool smooths the selected vertices by averaging the angles between the faces. After using the tool, options appear in the Toolbar:
The number of smoothing iterations.
Limit the effect to certain axes.
Adjusting the smooth option after using the Subdivide tool results in a more organic shape.
The Smooth Modifier, which can be limited to a Vertex Group, is a non-destructive alternative to the Smooth tool.
See the Laplacian Smooth Modifier for details.
Laplacian smooth uses an alternative smoothing algorithm that better preserves larger details and this way the overall shape of the mesh. Laplacian smooth exists as a mesh operation and as a non-destructive modifier.
Real Smoothing versus Shading Smoothing
Do not mistake this tool with the shading smoothing options described at this page, they do not work the same! This tool modifies the mesh itself, to reduce its sharpness, whereas Set Smooth / Auto Smooth and co. only control the way the mesh is shaded, creating an illusion of softness, but without modifying the mesh at all...