It's called the Casimir Effect and, even though this simplified explanation works, the effect still isn’t fully understood. The key word here is “uncharged.” If the plates were charged it wouldn’t be a surprise for them to attract or repel each other. The reason the two plates attract each other has to do with the "vacuum" component of the system. According to quantum field theory, even a vacuum has electromagnetic (EM) waves present throughout. Outside the plates, these EM waves would be able to have a wavelength larger than the distance between the two plates while, between the plates, these wavelengths wouldn't have enough rom to exist. This means that there would be more energy outside the plates than between (from the waves with larger wavelengths) and this difference in energy is the reason the plates would attract.
