So Proxies are a clever way of rendering a large number of objects, without crashing your main viewport. By exporting a mesh into a proxy and setting up your viewport to have an insane number of objects, you can render a scene with much more ease in the viewport. The only catch with this is whilst you can still see the all the objects, you can only see their bounding boxes. So you might not have as much control as you would if you could see the models.
Also, the convert tool is hand for converting more or less anything in Maya. You can turn Polys into Nurbs or a Paint Effect in Polys. I could definitly see how this would be handy.