im no expert, i can only tell you the difference i notice...
oftentimes i prefer natural lighting for "mood" portraits and such .. but sometimes im going for a more brighter, "magazine" look ... sometimes natural light just doesnt do it ...
i know for my "self" portraits (since im of darker skin with bright red hair) ... most of the time i come out underexposed if its later than 4pm shooting indoors with natural light
tonight my hubby and i were shooting "self" family portraits ... he's a bit brighter than me ... so most times he's overexposed and im underexposed ... so i have to put the strobe near me to take it up a notch
Ok, here's the gist of my research til now... from what I am reading, such as this thread at photo.net, strobe is another term for a flash, although mainly used when off camera. So it's like your continuous hot studio lights, except they are flash instead of continuous. That thread has a LOT of info in it, relating to portraiture and use of strobe.
I also found a lot of info about strobe and high speed and underwater photography, as strobe is very good at providing a lot of light, allowing really fast shutter speeds to stop action.