Inherit allow you to transfer the level that you already enhance an equipment to another equipment. So incase of upgrading weapon from level 20 to level 30 you simply transfer almost all the enhancement already been from previous equipment into the new one.
This process can save up all the hussle of enhancement equipment all over again.
Inherit pass 70% of the invested silver from old gear to the new gear. There is an option to transfer all the shell as well.