Fluorescence is the phenomenon whereby molecules that have absorbed near ultra-violet or visible light, emit light at a longer wavelength (usually in the visible spectrum). One may question where the extra energy goes; in some case, for example, it goes to vibrational energy (i.e. thermal decay).
In experimental practice, this is of very good use for imaging. You can shine light of the appropriate wavelength so that fluorescence occurs for the molecule you want to image. Then, if your image capturing device only works for a certain wavelength range (in this case, the range of the emitted light from fluorescence), then your imaging device will not "see" the original light that was shining on the entire sample.
Figure 1 shows an example of a fluorescence image. In particular, it is an image of a cloud of laser-cooled Rubidium 85 atoms from the Kuzmich group at the Georgia Institute of Technology.
 B.H. Brandsden, and C.J. Joachain, "Physics of Atoms and Molecules," Second Edition, Pearson Education Limited (2003).
 A. Kuzmich et al. http://www.physics.gatech.edu/qoptics/currentresearch/quantumrepeaters.html