The answers here are a bit incomplete by being very software focused.
A software problem that caused the processor to be very active and generate a lot of heat then exposed a flaw in their hardware and phone design.
Most computers are designed such that their processing power is incapable of overheating, through better cooling matched for the heat generation and sophisticated performance throttling to reign in temperatures. For example, I can run my folding rig for literally years on end completely maxing out all cores on the CPU and GPU with the most intensive processing possible, and the hardware handles it just fine.
The root of this issue is that the thermal power output of the processor in that phone model is higher than the thermal dissipation of the phone. Apple may have done this anticipating high loads to come in bursts (which they do), and wanted to minimize size, use materials for aesthetic rather than heat dissipation, and pack in more short term/burst power than the phone should handle.
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