Laser light shows the unique property of coherence. This is due to the stimulated emission process of photons. But why is it that stimulated emission leads to coherence?
In this link stimulated emission is explained in the third page:
Note that the energy of the incoming photon doing the stimulation is $E_2-E_1$ the two energy levels . This means the first photon passes and a second one comes out, which when conditions are appropriate can lead to the lazing phenomenon.
This is with pictures and words, but coherence is a mathematical phenomenon. It means that one has solved the quantum mechanical problem and wavefunctions exist which have a fixed phase between them, the definition of coherence:
In physics, two wave sources are perfectly coherent if they have a constant phase difference and the same frequency, and the same waveform. Coherence is an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference.
Now you ask:
But why is it that stimulated emission leads to coherence?
Because of the mathematical solution of the quantum mechanical wave equations of the problem, it comes out in this situation that the waves are coherent. One has to dive into the mathematics if really wanting to understand how it happens.