Basically as it gets colder water exchanges energy with the environment and gets colder.
But once it reaches freezing temperature, it can no longer get colder and all the energy is used for the formation of crystals.
> But once it reaches freezing temperature, it can no longer get colder and all the energy is used for the formation of crystals
Water at freezing temperature can get much colder without freezing. https://en.wikipedia.org/wiki/Supercooling:
“Water normally freezes at 273.15 K (0.0 °C; 32 °F), but it can be "supercooled" at standard pressure down to its crystal homogeneous nucleation at almost 224.8 K (−48.3 °C; −55.0 °F).”
But the semantic point still stands. Boiling water is still water -- in the specific sense of H2O in its liquid state -- while ice is not. The complaint that frozen water has a single-word synonym while boiling water does not is making a false equivalence.