In the real world, there is no such thing as "observation" in a strict sense. In order to observe something, there must be some interaction. For example, when you see a car, light is bouncing off the car and into your eyes. That light is an interaction.
So, you may still not be sold on the idea of the electron wave travelling through both holes, or the idea that electrons are actually quantum waves at all. So, let's put a detector at one of the two slits. What does this detector look like? Again, in very crude terms, it might be something like a constant stream of photons being aimed at one slit, and if some of the photons bounce off the electron passing through the slit, then we notice that some of the photons were disturbed, and from that we can deduce that the electron passed through that one slit.
When we do this, the interference pattern of "high, low, high, low" disappears. The pattern on the detector screen is simply flat.
In the language of quantum mechanics, very loosely, according to the Copenhagen interpretation, this is what happened. Without the detector, the electron wave travels through both slits, interferes with itself, gets an interference pattern in the wave, which causes the observed interference pattern on the detector screen over many, many trials.
When you add the detector, the interaction of the electron and the detector causes the wave function to collapse. After detection, the electron continues to travel along its merry way, but this new wave starts at one of the two slits, and therefore does not go through both slits, and therefore no interference pattern develops. The detector causes wave function collapse, and changes the scenario so that there is no electron wave that travels through both slits to interfere with itself on the other side.
Is this exactly right? No. I've taken some liberties, and I've chosen to use the language of the Copenhagen interpretation as opposed to other options.