I believe the main reason is to have the soap conform to whatever container/mug/bowl that you are using it in. If a soap does not come in a bowl (ex. Col. Conk) or you happen to have a "favorite" bowl that you would prefer to use, then this is a useful technique. Before reading of this method, I could easily get frustrated chasing my soap around the bottom of a bowl while trying to load my brush.
I USED to be a big fan of melting soaps, until Sue from Saint Charles Shave pointed out it was possible that damage could be done to the soap. I now recommend that before melting, use the soap. Otherwise, you may not get the results you would have, thereby finding a product less than satisfactory. Then if you still feel the need to get nuclear, give it a shot. At least you will have a comparison. Just remember, not all soaps can be melted, and you do so at your own risk!
Basically I melt soaps because my mug is 3.5 inches in diameter, and the little cake will dance around, and make it a pain in the neck to get a decent lather out of.
I have found that in short order, you can quickly find out if it is a "meltable" soap. For me, basically, I stick my fingernail into it, and if it penetrates without much pressure, and is a soft soap - I know I can melt it in the microwave. ALL soaps can be melted (from what research I have done on the net) however some will require a double boiler, which is a pain in the rear. Basically, I melt Col. Conk, surrey, glycerin soaps, and Pirate's Cove soaps. The key is to MIX the soap as it hardens after melting it (refer to the picture in my Pirate's Cove review with the bamboo skewer) as it will keep all of the components of the soap "mixed" and the essential oils will not clump together on the top. I have tested melted VS unmelted soaps side by side (same brand and scent) and have found NO difference between melted and unmelted form. The Pirate's cove I had actually lathered once before un-melted, as I had given a cake of it to Nick, and lathered it up to see how it performed, and to check out the scent.