The big picture is that matter transitions from states of high energy to low energy, and when they do that, they release a photon of a specific wavelength.
But, if you can keep enough of those atoms at a high energy state, you can do something called “stimulated emission”, where a photon passing by your high energy atom can cause it to release its photon at exactly the same phase/frequency/direction as the first photon. Then, if you put some mirrors on either side, you can make both of those photons bounce back and forth between your sample.
Both of those photons can then cause stimulated emission on the other high energy atoms, and then you get a cascade of photons, all in exactly the same phase, and at exactly the same frequency and in exactly the same direction. Then, you poke a tiny hole in one of your mirrors, and you can point your laser at something.
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