The term secondary eclipse is commonly used for a transiting planet's passing behind the body that it transits. If the planet is in a circular orbit around its host star, it also passes (at minimum, partially) behind the star, and does so in many possible elliptical orbits as well. The adjective "secondary" is a bit redundant and it is sometimes referred to as "the eclipse", but in discussions, the transit itself may be referred to as the primary eclipse.
Secondary eclipses are detected by an additional dip in the light curve of the star during the orbit of the extra-solar planet: a shallower dip than that of the transit: the typical reductions have been cited as 0.01-1 percent for the transit and 0.001-0.1 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:
A type of 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. For such an offset specific to particular wavelengths that could be the peak of a credible black-body spectrum, the offset can be interpreted as an indication of the location of the hottest spot on the planet's surface, which in turn, can reveal information about the planet's rotation and/or zonal wind patterns.