Imagine that you have a big bucket, and you dump a crapload of marbles into that bucket. This is sort of the molecular level of what’s going on when you pour a molten metal.
Much like any loose collection of small objects, the marbles sort of just fell wherever. There are spots where the marbles are more densely packed, but there may also be spots where there are gaps between the marbles (IE structural weaknesses in the metal at a molecular level). What you want is for this bucket of marbles to be situated perfectly to do something, so you find a way to settle the marbles into place.
To do this, you just need to introduce them to the right amount of energy. Vibrating the bucket (or heating the metal) causes the marbles (molecules) to settle into their optimal places. Too much vibration and marbles will spill out (metal fractures, etc), while too little means that it won’t settle properly.
Each metal has its own sweet spot for tempering temperatures.
TL;DR: Tempering is used to ensure that a metal object is structurally consistent on a molecular level, thus strengthening it as a whole.
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