It's well-defined mathematically but ill-defined philosophically. There is no agreement on what an "observation" is -- that is what is ill-defined:
> The Copenhagen interpretation is the oldest and probably still the most widely held interpretation of quantum mechanics. Most generally it posits something in the act of observation which results in the collapse of the wave function. According to the von Neumann–Wigner interpretation the causative agent in this collapse is consciousness. How this could happen is widely disputed.
It's an open problem, and I'm not sure if there are official tallies, but I think that currently most people think that the explanation is decoherence instead of consciousness. From the same Wikipedia page:
> Erich Joos and Heinz-Dieter Zeh claim that the phenomenon of quantum decoherence, which was put on firm ground in the 1980s, resolves the problem. The idea is that the environment causes the classical appearance of macroscopic objects.
> The Copenhagen interpretation is the oldest and probably still the most widely held interpretation of quantum mechanics. Most generally it posits something in the act of observation which results in the collapse of the wave function. According to the von Neumann–Wigner interpretation the causative agent in this collapse is consciousness. How this could happen is widely disputed.
https://en.wikipedia.org/wiki/Measurement_problem