What is a wavefunction, in the context of String Theory? I have to admit that I don't know much about String Theory (or QFT, for that matter ..), but, if we assume that String Theory is the correct description of fundamental particles, what is the correct way to think about a wavefunction, in the context of String Theory?
For example, take an electron being shot from an emitter to a target. I usually imagine the wavefunction as spreading out from the target in three dimensions, possibly traveling through two or more slits; interfering with itself along the way; and then spontaneously deciding to collapse down onto one of the atoms that makes up the target surface. Where does the string fit into this picture?
Does String Theory say anything about the mysterious wavefunction collapse? (I assume it must do, otherwise can it really be described as a 'theory of everything'?)
Edit:
It was mentioned in one of the answers that, in string theory, 'point particles' are described as strings. Hang on though .. in QM we were told: "there are no point particles, there are only wavefunctions." But, now in string theory, apparently these point particles are back again, only they're now described as strings. So, where did the wavefunctions go?
 A: I think one important thing to mention is that Copenhagen Interpretation of Quantum Mechanics is not the only interpretation out there; in particular there is no "need" for wavefunction collapse if you don't want it. Alternative interpretations include the Many Worlds Interpretation (which makes sense in light of the development of Decoherence in quantum theories; for more on this interpretation I'd recommend this paper by Max Tegmark). 
I don't think String Theory should be viewed as something that can resolve between different interpretations of Quantum Mechanics; after all String Theory is still a Quantum Theory. In particular, you still have wavefunctions as before; but instead of describing what you might think of as 'point particles', they describe strings.
A: One of the tenets of quantum mechanics is that the wave function characterises fully the state of the system. In other words, all you can know about a particular system is encoded in the wave function.
So in the case of a point particle, the wave function encodes the probabilities of its position, momentum and energy. The electron also has spin, so the wave function encodes information about that too.
In the case of a 1D string, instead of measuring the position, one might ask “what is the string’s vibrational state”? So the wavefunction encodes that too. 
Now, note that your way of thinking about the wavefunction of a particle as something spread out in physical space  only works in the case of a single point particle! Already for the simple case of a particle with spin 1/2 you would need two such wavefunctions (one for the spin up and one for the spin down). I won’t go too deep into it, but the wavefunction of a system is a function that assigns to each result of (compatible) measurements, a complex number.
So back to the point particle case, the $\psi(x)$ is a complex number assigned to the position $x$. So you can confuse it with, or think of it as, a function on physical space, even though it is a function on the possible results of measuring the position.  In the case of a two particle system, the wavefunction is of the form $\psi(x_1, x_2)$ so its a function from the 6 dimensional space of pairs of 3D vectors $(x_1, x_2)$ to the complex numbers. Good luck thinking of this as a function on physical 3D space!
With regards of “what is real” in quantum mechanics, the jury is still out. The maxim “there are no point particles, only wafefunctions” is a bit misleading. While it’s true that you can’t reason correctly about quantum systems as simple billiard-ball-like point particles moving in potentials, not everyone would agree the wavefunction is real, or physically real, whatever that might mean for them. The wavefunctions are essential tools for reasoning and calculations, but you can’t think of them, consistently, as physical objects out there in physical space, like one might think of sound waves or light waves.
A: To link these theories one must imagine these physical strings as an extra dimensional connection through space/time vibrating, spinning, tumbling, on the wave function, connected through "time" and not observable by humans. They appear as points or particles in the present of our consciousness which is the only part of spacetime currently observable to humans. These point particles are actually points or ends of the strings where they occupy our observable point of spacetime in the present. Which is where the stream of human consciousness lies. Technically the strings are real, just not observable to humans as we don't experience time in that way. So the wave function is the motion and energy at which the strings are moving and showing the possibility at which any point on them might be observed in a particular point/place/time in spacetime. Technically connected with energy through time from the moment of the big bang through the present which we observe as points and on through to the future. You really have to have a firm grasp on time being relative and the link between space and time and spacetime as a dimension to understand string theory. Donny Darko offers an interesting illustration of time travel and a little bit of string theory in the visualization. For humans to actually observe the strings we would have to be able to manipulate the flow of time or experience it as a more holistic connection than a flow from psst through present to the future. We would have to be able to simultaneously observe more than just the present.
