The Connect surface tool by Dimitri.

[Dimitri]

I am putting below an image too (although the image in Blender's link is demonstrating the whole thing very clearly). The request is very easy to understand: you just pick two vertices on a mesh, you click 'connect' and, voila, you have a connecting line between the two... a line which has connected them following the shortest distance between them on the surface of the object.

(here the turquoise line is denoting the two vertices to be connected and not the actual line that will created on the object's surface of course)