A transiting planet is a planet crossing between an observer and an astronomical body. Examples are Venus transiting across the Sun, any solar-system planet crossing in front of a star, or an extra-solar planet crossing in front of its own star.
Such transits constitute one of the methods by which exoplanets are identified: light from the star is reduced by the amount of light blocked by the planet, typically on the order of .01% to 1% for the transiting planets currently being discovered. Discovering possible transits can be automated by automatically surveying a lot of stars repeatedly, looking for differences in brightness. The Kepler space mission is one such initiative.
What seems like transiting exoplanets may be transiting binary stars: if either star is behind the other, light from the pair will be dimmed, and the dimming can happen periodically. Thus, the need for confirmation that the observation truly is a transiting planet, through analysis and further observation. One sign suggesting a planet is that a planet blocking the star's light will (generally) block all colors (an achromatic transit) whereas a transiting star is likely to be producing a different spectrum, so that at different wavelengths, the amount of dimming will differ. Thus, observations of the transit at two different colors to compare the amount of dimming is a method of eliminating some phenomena that appear to be a transiting planet on first observation.
EMR from the transiting planet can be studied through study of the spectrum through a cycle that occurs through each orbit, i.e., comparing when the dark side of the planet is toward Earth to when the light side is visible. It is also studied through the slight change in magnitude and spectrum during the secondary eclipse, i.e., the planet passing behind the star. Current such observations deal with reductions in the range of .001% to .1%.
Atmospheric makeup has been studied by comparing to what percentage of each wavelength is blocked during the transit (probably smaller changes than would be expected by a binary companion), assuming a partially transparent atmosphere forms a ring around the opaque disk of the planet and the affect of the atmosphere on the transmitted EMR can be determined. Some conclusions can be drawn from absorption lines and more by comparing to models of plausible atmospheres. The direction of the incoming rays from the star, as affected by refraction must be taken into account.