The term secondary eclipse is commonly used for a transiting planet's time behind the body it is transiting. If it is in a circular orbit that transits its host star, it also passes (at minimum, partially) behind the star, and often does so in elliptical orbits as well. The adjective "secondary" seems redundant and it is sometimes referred to as "the eclipse".
Secondary eclipses are detected by a dip in the light curve of the star through the orbit of the extra-solar planet: a shallower dip than that of the transit: the relative sizes of the dips have been cited as .01 to 1 percent reduction for the transit and .001 to .1 percent for the secondary eclipse, numbers which naturally incorporate the selection bias that sufficiently small dips wouldn't be detected. Characteristics of the observed secondary eclipse data reveal information about the planet:
Spectroscopy using the secondary eclipse is known as occultation spectroscopy and uses differential spectroscopy, i.e., comparing the spectrum of star-plus-planet during the eclipse with that at other points in the planet's orbit.
An eclipse timing offset, is the offset between the timing of the observed dip in the light curve compared to the expected time of the eclipse. If an offset is specific to particular wavelengths that could be the peak of a credible thermal emission, the offset can be interpreted as an indication of the location of the hottest spot on the planet's surface, which in turn, can be evidence of the planet's rotation and zonal wind patterns.