Quantum theory describes the behaviour of the smallest parts of matter. It was developed by a cluster of European physicists in the early 20th century - notably Niels Bohr, Max Planck, Werner Heisenberg and Erwin Schrödinger - and it completely changed our understanding of how the physical world operates. Quantum theory reveals the strangeness at the heart of ordinary things - light, for example, can be seen both as particles and as waves; and particles only interact with other things with a certain probability, not with any certainty.
Without this theory, we would have no transistors, no fibre-optic cables (and therefore no high-speed internet) and no lasers (so no CD or DVD players). But the theory was invented because of the pure inquisitiveness of scientists. Quantum theory is perhaps the perfect example of how pure research can come to have huge effects on our whole world.
Quantum theory was important for the development of both atomic power and nuclear bombs. It has also been used in new technology such as GPS.