It is an effect of the non-linearity of the first stages of the amplifier. What actually happens is that when high-frequency signals are seen by the entrance of the audio amplifier, the amplifier cannot follow the very high oscillations. Normally, you'd say, don't worry, that means it gets filtered out. That is correct if the entire system is linear. But the signals from a cellular phone are MODULATED high-frequency, and due to small non-linearities in the amplifier, you change slightly the operating point because of the incoming signal. Now, that, in itself would not be a problem, but the movement of the operating point follows the modulation (it moves, say, slightly up when the signal is present, and moves down again when the signal is not present). And as such, the modulation signal becomes amplified.
It is exactly the same principle as an old AM radio, where you use a (non-linear) diode to "detect" the modulation. Given the rather high power a cellular phone uses for his broadcasts, this is seen by the audio amplifier. Any AM radiostation nearby would do the same. FM wouldn't because the envelope is at almost constant level.