This concept is often confusing for initiates to quantum mechanics. The wavefunction should not be viewed as an inherent property of a particle or a system. Rather, it represents our knowledge of that particle or system.
The wavefunction is nothing more than a probability distribution. If we know nothing of the state of a system, it might be anything, and therefore the probability distribution would be very broad. However, if we know some of the properties or boundary conditions, the wavefunction can no longer be anything, it must adhere to those conditions. Therefore, the more we know about a system, the more sharply peaked the probability distribution, and hence the wavefunction, will be.
The collapse of a wavefunction does not necessarily change the system or particle in any special way. However, since real-life measurements tend to influence the system, and wavefunctions are closely related to phenomena like interference patterns (take for example the double slit experiment), one might think that it is an inherent property of the system.