Quantum is a criminal organisation that appears in two James Bond films, Casino Royale and Quantum of Solace. The organisation goes on the missing in action list for Skyfall. However, the organisation is back, well, at least the head of the organisation Mr White is back, looking very dishevelled for Daniel Craigs fourth appearance as James Bond. It is led by a man calling himself Mr White who appears in both films.
Quantum are not an out and out terrorist organisation, instead they provide services to terrorist organisations. In the second film, the C.I.A. are shown to be dealings with Dominic Greene regarding the future of Bolivia.
Unlike SPECTRE, Quantum was never about bringing about the end of the world. Quantum was into sparking revolutions but always keeping under the radar , not one for mass world wide hysteria that a mad man with a space technology ( Diamonds are Forever ) would have. Unlike SPECTRE, they never quite managed to get space.
Whether Quantum is destroyed or merges or becomes SPECTRE is not yet known until the Spectre comes out in 2015.