Yep, Mad's right. The main advantage of the parting tool behind the work is having it mounted upside down. That way you don't have to run your lathe in reverse and even more importantly, the chips fall away from the parting grove rather than filling it up. 

This setup can also be helpful if you are machining multiple small parts of the same type. Lets say you had a piece of round stock that you needed to face, turn, drill, and part off. And you needed to make 10 of them. You could face and turn with the same tool (of properly ground and set at the right angle). Then you could move that tool out of the way and drill with your tailstock. Then you could move the cross slide toward you bringing the upside down (and on centerline like Mad mentioned) parting tool into contact with the part, parting it off without ever turning your lathe off or reversing the spindle direction.

This setup saves you the step of swapping the facing/turning tool with the parting tool. Some even say that you'll get less chatter with the parting tool upside down. But you'll have to make sure that your gibs are set nice and snug (but still free moving) because the parting tool will be pulling up on the cross slide instead of pushing down.

Some lathes with longer cross slides are more suited to this setup. The lathe Harold uses (a Myford 7 if I remember correctly) is set up well for this purpose because it has a large cross slide with T-slots. My lathe has a short cross slide platform and no T-slots. So I'd have to actually machine a new longer cross slide base and either machine T-slots into it or bolt a parting tool directly to it – neither of which I want to do. 

Hope that helps!