Fluorescence resonance energy transfer (FRET) is the process that permits probes to emit fluorescence only after hybridization and describes the energy transfer between two fluorophores.
Each probe consists of both a donor and a reporter fluorophore with the donor being on the 3' end and the reporter on the 5' end. The proximity of the two fluorophores to each other allows for the donor to reduce the fluorescent state of the reporter. When the probe attaches to the single-stranded piece of DNA, the fluorescence is still being suppressed. As the polymerase takes effect and begins to synthesize the new complementary strand of DNA, the reporter and donor fluorophores are separated. This separation allows for the reporter to emit its energy, which is picked up by the computer. The more denaturing and annealing that takes place, the higher the fluorescence in the tube.
The process of FRET can be compared to the classic science experiment using tuning forks. If you strike one tuning fork so that it rings and hold it near a tuning fork that has not been struck, it will begin to ring by the force of the resonating waves from the initial tuning fork.