What does fluorogenic mean for fluorescent probes?
The usage of "fluorogenic" is typically applied to probes that are not currently fluorescent but can be, typically by some enzyme action or other reaction. For example, see here, here, or here. Essentially they are precursors to the fluorescent molecules of interest. 

As one example, you could get a higher signal to noise ratio if you only "activated" the fluorogenic compound in one area, perhaps inside cells vs in the extracellular space, for example, so you aren't dealing with stray light from that "unwanted" signal.

References:

Shieh, P., Hangauer, M. J., &amp; Bertozzi, C. R. (2012). Fluorogenic azidofluoresceins for biological imaging. Journal of the American Chemical Society, 134(42), 17428-17431.

Lukinavičius, G., Reymond, L., D'Este, E., Masharina, A., Göttfert, F., Ta, H., ... &amp; Blaukopf, C. (2014). Fluorogenic probes for live-cell imaging of the cytoskeleton. Nature methods, 11(7), 731-733.

Friscourt, F., Fahrni, C. J., &amp; Boons, G. J. (2012). A fluorogenic probe for the catalyst-free detection of azide-tagged molecules. Journal of the American Chemical Society, 134(45), 18809-18815.