To a physicist, water at room temperature is not terribly interesting. Neither is ice at 20 below. But the transition that occurs from one phase to the other at 0C now that's something to behold. The natural world is full of such phase transitions.
Crystals reconfigure themselves as pressure or temperature changes.
Biological systems can undergo snap transformations. Phase transitions and the computational complexity they bring may help explain why artificial intelligence programs sometimes bog down. It's too early to claim that it actually works, but it has the potential for that. Boolean expressions are created by combining logical variables with ANDs, ORs, and NOTs. Short expressions are usually satisfiable, but longer, more complicated ones, in which the same variable may appear many times in different contexts, often are not.