That picture explains a lot. I think I can describe a few things that will help understand what you see on the scope.
First, there's the physics of the thing. The voltage you measure is produced by "electromotive force" or EMF, and that is generated by a change in flux that passes through a closed loop of wire. There's a lot going on in that statement alone, and I could go into the math of it but for now the verbal description may be enough. I want to emphasize the word "change" in that definition. What that means is that flux can pass through the coil, but if it doesn't change, then you get no voltage. No voltage, no current, and so on. The change in flux is for all of those field lines to move toward and away from the coil. In the case of your alternator, they pass by as the disk rotates, and the next magnet that passes by has the field lines pointed in the opposite direction. Reversal of the flux gives you a reversal of the voltage.
Next, there's the more detailed look at the changes as the magnets pass. At a moment that a magnet is aligned between two coils, then there's a bit of overlap of its face over the coil, but on the other side is the opposite side of the coil is the other magnet, pointed the other way, so the total flux through any coil cancels out. Zero flux.
Next, move the magnet rotor a millimeter clockwise. Let's say it's the N magnet that moves a little further over the coil. And so then the S magnet face moves a little farther away (actually it is moving over the next coil). More N pole on that coil give more + flux. That's a change in the flux passing through the coil and you get a EMF from that, which you can measure as voltage.
Next, move the N magnet a few millimeters farther again. A bit more N flux on this coil, and the S flux is mostly over the adjacent coil too. Still adding + flux to the coil we're looking at, so the change is + and there's still an EMF.
Next, move the N magnet farther, and now its face is entirely superimposed over the coil. That S face has moved entirely over the other coil at the same time. We have the most + flux now, but that last bit of movement didn't actually add much, it just made the corners of the rectangle cover the coil better. It wasn't actually as big a change in + flux as it was before, so there's actually a bit less EMF. It's still increasing, so still + stroke on the voltage, just not as much as before.
Next, move the N magnet farther. Well it's still all superimposed on the coil, which is bigger than the magnet. The same amount of flux is passing through the coil as it was a moment ago. The flux didn't change. The EMF is zero. The voltage has dropped to zero for a moment.
I think you get the picture by now. There are spots where the EMF goes to zero for a period of time, there are spots where the EMF is changing but at a fairly constant rate. These cause the voltage on the waveform to go through zero, and to flatten out at various times in the cycle.