So Vanity Weapon Slots.

[Sumii]

What is this transmog and transmutation exactly?

Transmogrification is the 'vanity system' from WoW. You have an ugly weapon with awesome stats. You have a nice looking weapon with crappy stats. Put the ugly weapon as the base, and then drop the pretty weapon to the right. Hit a button and the pretty weapon's skin is applied to the ugly weapon. You can always reset the ugly weapon back to its normal skin.