The vertex snapping is for snapping a specific vertex or pivot point to a object having a mesh to an another vertex or a pivot to an another object.
How to Use
In order to use the vertex snapping the editor mode should be switched to Vertex Snapping Mode by clicking "Vertex Snapping" button on the Object Toolbar.
After entering Vertex Snapping Mode, select the first vertex or a pivot point. (The blue cubes are vertices and a red sphere is a pivot point.)
Then drag the selected vertex to the target vertex of another object:
The objects are now snapped:
If you are having trouble selecting the required vertex, adjust the camera position to get a better view.
To exit Vertex Snapping mode, press escape to return to normal editor mode or clicking the vertex snapping icon.
In preference "Vertex Cube Size" can be set. It affects the size of each vertex cube and the pivot point sphere.
The vertex cube size is adjusted automatically according to a distance from a camera so that the cubes are drawn as uniform sizes in a screen view.
And normally the vertices of objects around a mouse cursor are drawn.