That “stuff” is the miso, fermented ground beans or grain. The clear broth around it is dashi made from kombu or dried kelp, and bonito, which is dried, and sometimes fermented, tuna.
The reason it forms those rather attractive ethereal shapes in the bowl is because of currents of hot dashi rising up the centre of the bowl, cooling, then flowing back down the edges.
Here is a traditional miso haiku:
Hot miso forms clouds
ever forming never rain
in a bowl of soup