To expand on what the others have said, your Regulator-Rectifier (R/R) is what sets the approximate charging voltage. For an alternator, it's an alternating current (surprise surprise), and it basically cuts off when the voltage get too high, and cuts back in when it gets too low. But since it's always cutting in and out, it will jump around.
Your battery, however, acts as a capacitor and will smooth out the voltage. This is why you should never run an engine without a battery. You could start it with the battery and then take the battery out, but the voltage spikes will likely damage the electronic components. Battery eliminators are designed to fix this by providing a capacitor to act as if the battery was there, even if they don't provide any power.
So if your R/R is going, it might let too much voltage though and it can spike. If some components (battery, R/R, or the engine) aren't grounded properly, your battery will not act as a capacitor very well, and could give the same symptoms.