I've been curiously interested in Bell's Theorem for years now. To get a laymans view, read this well written article on the subject. Basically, there is a trick in quantum mechanics where two particles can communicate with each other over an infinite distance literally instantaneously. Unfortunately, there a properties of this trick that make it appear impossible to harness for instantaneous communication.
The reason that this is interesting is that instantaneous communication would change the world as we know it. Right now we take communication as instantaneous because light can loop around earth in less than a second and we can communicate virtually at the speed of light. But this is still a huge limit.
Latency between networked computers make it nearly impossible to build general-purpose supercomputers that operate in multiple places in the world. These constraints even cause issues when the computers are talking to each other across the room.
Communication off planet - to satellites, astronauts, mars rovers, you name it, is delayed. To talk to someone on mars, it takes a 6.5 minutes minimum to get a message to them[link].
Even terrestrial communication is limited by non-instantaneous communication. As long as there are wires (or fiber, or whatever) between two points that are communicating, communicating at the speed of light is relatively cheap. If you try instead to use radio communication: satellites, wireless internet, cell phones, radio, the expense of communicating in terms of energy quadruples every time you double the distance you are trying to communicate. This is why cell phones only have a mile or two range from a tower and wireless internet only works for a hundred feet or so. Imagine every cell phone or computing device having communication without wires, with long battery life, and no towers. That cell phone then works anywhere, whether you are in an airplane soaring miles in the air over the pacific, in a cave, or in a submarine on the bottom of the ocean. The communication would also be undetectable, untracable.
An exciting idea. And Bell's Theorem tells us that quantum particles do this all the time. Too bad nobody has figured out how to harness this.