What is a wave function? It is a mathematical function depending on energy and momentum or space and time,$Ψ(p_x,p_y,p_z)$ or $Ψ(x,y,z,t)$ ( in its simple form). This function is a solution of a wave equation, a second order differential equation.
Mathematical functions are a billion, what is the wave function's connection with measurable physical quantities? The connection is postulated axiomatically in the postulates of quantum mechanics¨, $Ψ^*Ψ$ is the probability distribution of the products of the interaction; this means that a number of measurements have to be done with the exact boundary conditions to get an experimental distribution to compare with the theory that has calculated the wavefunction. So the mathematical function itself is not directly attributed to a given event, so it cannot be measurable.
How is a measurement performed?by interaction. Each interaction changes the boundary conditions, and thus the specific mathematical $Ψ$ is different before or after the measurement. That is what the collapse is, change of the specific wavefunction.
I will continue
It says that for a given boundary condition physical problem the