Förster / Fluorescence Resonance Energy Transfer (FRET) is the non-radiative transfer of energy from a molecule in the excited state (donor) to a molecule in the ground state (acceptor). A fluorescent donor molecule can return to the ground state by losing its energy through emission of a photon (fluorescence), or by transferring its energy to a nearby (1 - 9nm) acceptor molecule (FRET). Compared to a molecule that exhibits no FRET, the donor has more options to lose its energy. Therefore, it returns faster to the ground state, which decreases its lifetime.

To let FRET occur, the emission spectrum of the donor fluorophore has to overlap the excitation spectrum (absorbance) of the acceptor fluorophore. Some examples are BFP-YFP, CFP-YFP, GFP-DsRed, GFP-Cy3, GFP-mOrange, YFP-RFP, and Cy3-Cy5.

Browser based calculator to find the critical distance and FRET efficiency with known spectral overlap.

FRET efficiency $$E$$ indicates the percentage of the excitation photons that contribute to FRET and is defined as: $E=1-({\tau_{DA}\over\tau_D})$ where $$\tau_{DA}$$ is the fluorescence lifetime of the donor in the precense of an acceptor, and $$\tau_D$$ in the abscence of an acceptor. As you can see, the more FRET occurs, the more decrease in donor fluorescence lifetime.