What does it mean to observe? This is a layman's question. The only thing I know about quantum physics is from casual reading and documentaries. I can imagine electrons being probabilistic waves.
Their position is an infinite number of weighted points and only upon observing the actual position do we know which of those points was its actual position.
I program in Haskell so I imagine the concept as laziness. Only upon actually needing the information, we get it.
But what does observing actually mean? In Haskell I can treat a lazy value as if it were already there and manipulate it as such. One way of starting the actual evaluation is by printing some value, this then causes all the values that are depended on to also evaluate, then all the ones those depended one and so on.
I figure the universe isn't that human centric and "observing" means something other than actually seeing something, but the quotes like "I like to imagine the Moon being there even when I'm not looking at it" make me wonder.
 A: It is worse than lazy evaluation.

Haskell I can treat a lazy value as if it were already there and manipulate it as such. 

In quantum mechanics you can't do that. What you have is something that tells you the relative frequency of getting lots of results for different interactions if you did one of the various interaction first.  And you can't do them all first.
For instance you could model the spin of an electron with a vector. The lots of interactions could then be having the electron pass through some regions of inhomogeneous magnetic fields that the electron could pass through transverse to the field.  There are lots of different interactions because there are lots of possible fields. Each field is aligned in a particular direction and after passing through the field inhomogeneity the beam will be spilt into two beams and one beam will have the spin vector change to be aligned with that field direction and the other beam will have the spin vector change to be anti aligned with that field direction.
But the sizes of those two split beams is related to how close the original vector was to pointing in either of those field directions.  And in particular if the original spin vector was pointing in exactly that field direction then the split beam that ends up with the opposite pointing soon gets no size and the one with the matching spin gets it all.  And this happens in a continuous way, so if the incoming spin vector points almost entirely in that field direction then almost all of the beam gets sent in the direction where it gets polarized to point that way.
So what we call an observation is really an interaction that changes it but changes it in such a way that if you immediately repeat the interaction again you don't change it again.
So there is some repeatability.  If the original beam could split into two beams then post measurement the resulting beams each individually can't split into two beams (for the exact same type of interaction). So it is definitely changed (unless it happened to already be in one of those output type final states to begin with, in which case you find out which one it is in because if there is only one beam then a particle detector placed where there is no beam will not go off).
So in general, lots of states are possible. Only some states are possible after a measurement.  If it happened to be in one of those final states you can find out which one it was in. But it instead could have been in a final state for a different kind of measurement (say for example if someone previously observed it for a field aligned in a different direction).
It is simply impossible for it to have the initial state be in one of those "final states" for every possible interaction. Hence you can't assume it has a preexisting value for the outcome of those different interactions.
We should call it polarization or some other word rather than observation. But then it wouldn't sound as spooky and mysterious. Well, really things just get bad names for historical reasons.

Here's how I interpret what you're saying. An electron is a wave, if it enters some "fork" where depending on it's position different things could happen, it doesn't "evaluate" yet. It's position, as a probabilistic distribution, just gets deformed.

It is a complex wave and also a spin vector. Or else it is a wave that has a more complex object at every point that has enough information to tell you a relative phase, a relative magnitude, and a unit spin vector.
For the rest I will be describing a specific kind of so called observation, that of the spin of an object called a "spin 1/2" object.
There is a device that has an orientation and a calibration (not based on a spin vector, just based on the orientation of a magnetic field it produces and a direction in which the field changes). The orientation is a vector and the calibration is something I may or may not get to later, it might not be essential.
The device causes the electron wave to fork. The size of the branches in the fork are based on the relative orientation of the electron's spin vector and the orientation vector of the device. If they are orthogonal, the two branches of the fork are of equal size. If the orientation of the spin vector and the device vector are parallel then there is just one branch (but it still deflects left or right, depending on the calibration some devices calibrated to deflect left, some calibrated to deflect right). And if the vectors make an angle in between those extremes you have a relative size of the branches of the forks that is in between those two extremes.
Here is the essential part, which was not in your statement. As the wave progresses to the fork, the spin vector of the electron changes. the parts of the wave heading to those two branches evolve differently. 
The part that becomes the left branch evolves to point in a direction such that if that branch were sent to a similarly oriented and calibrated device it would all branch left again (with no right branch of the fork).  
And the part that becomes the right branch evolves to point in a direction such that if that branch were sent to a similarly oriented and calibrated device it would all branch right again (with no left branch of the fork).  
This repeatability is great for objectivity. It is a true shame however that we use the word observation for an interaction where we changed an essential part of the electron.
So back to the programming, we have no function that reads member data, we only have functions that split and change the objects.
Since the interactions change them it means doing it now or doing it later matters, doing it now or doing it later makes you get different results.
For instance if you observe with a device aligned with your particle's spin you just deflect it, and then you could observe it with a device orthogonal to that and you could split it into two.
However if you used the same devices in a different order then the one used first will splits it and then the next one used with split it again so you end up with four equal sized branches.
A totally different result. These are interactions that change things in nontrivial ways. And the order you do the interactions affects the results you get.
Note I haven't once mentioned probability since I quoted you. The probability isn't important. All of this is just from the Schrödinger equation, the interactions clearly aren't a passive observation of some preexisting quality.
And since which part of the beam when left or right depended on the calibration of the device then it in no way is something intrinsic to the electron it is an interaction between two things, and interaction that changes the electron.
It is best to pretend that the word observation was just a mistranslation from a different language because taking it literally as an evaluation or discovery of something about the electron will lead to actual errors in more complicated situations.
It is nothing more than an interaction that has a kind of repeatability. Nothing more. Nothing less.
A: Let me try to use a programming analogy.
A quantum mechanical object is like a class. 
It has certain attributes, which would be physical attributes, e.g. position, momentum.
It also has certain methods, which are physical operations that can change or modify the object or modify the environment using the object. In physical terms these are the unitary operations or measurements that can be done on system.
An experiment can then be setup just like a script. You can setup an experiment or script without having to instantiate a particular instance of the class. You can just use the dummy variable.
So far so good. Now you run the experiment and the analogy breaks down. The quantum script gives a different answers every time!!
The differences lie in the definition of objects and attributes and measurement. 
First, quantum objects with the same attributes are indistinguishable. In the class of electrons, you can instantiate many objects, but you cannot tell them apart, they have no labels. So you can have 1 electron or 10 electrons, but not electron 1, electron 2, and so on. 
Secondly, quantum attributes are not fixed precise values but probabilistic distributions. In fact by Heisenberg's inequality it is fundamentally impossible to measure two complementary attributes precisely. Therefore when an quantum object is created, it is not created with fixed attributes but with a probabilistic distribution of all its attributes.
Third, and very importantly, attributes need not be independent. Measurement is a method just like any other operation. Because attributes need not be independent, any method acting on one attribute can completely change other attributes.
Once you accept this new definition (which has held over a hundred years of experiments) it is easy to see what a measurement does. A measurement of one attribute simply 'collapses' its probability distribution into one possible instance. And every time you run the script, a different random instance of the object and its attributes will be drawn. Moreover, such a measurement can have drastic effects on other attributes or even other objects whose attributes are entangled with the measured attribute. 
To get consistent results from a quantum measurement, you must either devise an experiment that samples the distribution and rejects all but the acceptable instances (i.e. post-selection), or uses the properties of the distribution rather than the random instances for its processes. Both approaches are commonly used.
