“Battery” is a term for any system that holds potential energy for later use. Two connected lakes to power a dam is a battery. Holding a rock up high to power a pulley is a battery.
In the case of the battery you are thinking of, we have a small object with two chemicals closely connected but separated that have electrons (little energy balls) that really want to go from one of those chemicals to the other.
There are many forms of “power output”, spinning a motor, producing light, powering a magnet, activating computer cells, and they all will produce some amount of heat, as that is the most efficient form of expending energy (think friction).
A cheap battery is made poorly, meaning the barrier between the two chemicals is prone to failure. When that happens, there is no other form of consuming the energy, and so it all becomes heat.
Lots of heat in a small enclosed space means boom.
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