I'm curious about the underwater Internet infrastructure that interconnects continents to each other.
Can anyone elaborate on how it works, or any other details (such as security) of these wires?
This article by SciFi author Neal Stephenson is a not-bad introduction.
Wikipedia's article on Submarine Cables has a good overview as well.
Details of cables differ, but the Wikipedia picture is representative: a bunch of fibers in the middle, a lot of layers wrapped around to protect them and to provide power.
The fibers are single-mode (I think - I need to triple-check this and will edit this comment out when I do. They should be single-mode for the longer transmission range) and each will have several channels/signals multiplexed on to it using DWDM (Dense Wavelength Division Multiplexing.) Cisco has a detailed book on DWDM available on-line.
Repeaters are typically no longer used, instead the signals are amplified optically using EDFAs (Erbium-Doped Fiber Amplifiers.) The power for the lasers used in the EDFAs is carried by wires in one of the layers of the cable.
You can find more information scattered over Wikipedia links, e.g. fiber-optic communication, and some manufacturers of cable have some information available, e.g. Corning has some basics of fiber-optics here.