Okay, let's say you are a warder (Shaman/Warrior) who uses Primal Strike. As such you do lightning damage. However, you also do physical damage via weapon and skills. As a PS Warder your focus of skills are for lightning. Thus the physical damage you do isn't being buffed up. That's where conversions come in play. You can convert %'s of your physical damage to lightning and by doing so your damage for that physical attack will be converted to lightning and then buffed by the lightning buffs. Thus higher damage. I am sure some will have a more technical explanation, but that's it in a nutshell.
I will go out on a limb and guess that you may be actually a shaman and see the conversion to vitality on a passive (I can't off the top of my head recall the name of the passive, but I have seen it) That would be if you wanted to focus on vitality in your build due to the other class you selected for your build. Or... you simply wanted your build to fit a particular set that focuses on vitality. I hope this layman's explanation helps.