Minerals in water solidify when heated?
Limescale (calcium and magnesium carbonate) precipitates in the heater, the brown colour is most likely some iron compound that co-precipitates. A fresh surface of limescale likes to adsorb other ions, which then get trapped in it as the scale grows. If you had a water kettle, you'd see the same stuff in there after using it a few times. (Not exactly, because carbonate precipitation depends on the pressure, but iron (hydroxide?) not. I wouldn't want to predict.)

The limescale first appears on the surface of the heater cell, and then breaks off during temperature changes, i.e. when you open the faucet. As you have no tank, the flow rate of the water is high in the heater and carries the scale out of there.

Very convenient, that. In a tank, the scale builds up and can fill the whole thing after a few years, depending on your water source.