This is actually quite complicated and is related to physics, audio theory, psychoacoustics, and linguistics. From where I sit as a composer, the reason we hear either Yanni or Laurel has to do with what’s known as frequency response, which a measurement of amplitudes over a frequency spectrum.
It’s a term usually associated with microphones, speakers, etc…. For example, some microphones are equally sensitive throughout a spectrum (flat FQ response) while other microphones have a more shaped response, perhaps more sensitive to lower frequencies or higher frequencies.
Our ears are our “microphones”, and as such also have a frequency response. Some people are more sensitive to certain bands of frequencies, or groupings of frequencies, than other people. As we get older, this frequency response changes (remember the ringtone that only kids could hear a few years ago?).
In the Yanni/Laurel audio, there is something about the formant (the most fundamental frequencies of a sound) that obfuscates what some people hear in the Yanni/Laurel audio. Interestingly, if one lowers the pitch of the audio, more and more people will begin to hear “Laurel”, and if you raise the pitch most people will begin to hear “Yanni”. Likewise simply filtering out higher frequencies will result in more people hearing “Laurel”, and conversely, filtering out lower frequencies will result in people hearing “Yanni”.
What one might deduce is that those more sensitive to higher frequencies will hear “Yanni” of the original recording, and those more sensitive to lower frequencies will hear “Laurel”.
The NY Times has a more thorough explanation and a fun tool on their site that allows you to change the audio in real time: https://www.nytimes.com/interactive/2018/05/16/upshot/audio-clip-yanny-laurel-debate.html