Since you are a previous owner of the 430, you might simply explain what is it about the 580 which you do not understand? The 580 can be Master in wireless flash, whereas the 430 cannot. Apart from power and wireless, the two flash units are conceptually quite similar. Your OP is too open ended, and you need to advise what information you need, not merely "Please explain the meaning of Life".
In ETTL, the camera tells the 580 how much light to put out, after the preflash. The 580 tells the 430 how much light to put out, based upon the amount of light commanded by the camera and also based upon the flash intensity ratio which the photographer had established. In manual, the relative output of the two flash units based upon the Manual power setting of the Master and flash intensity ratio which the photographer had established.