A phase curve is the brightness of an astronomical body as a function of its phase, in the sense of the Moon's phases (full, half, quarter, new, etc.), but considering the body to have a continuous set of phases, one for each possible angle (phase angle) at the body between the direction of view and the illuminating body. Information can be gleaned from a body's phase curve.
The phase curve of extra-solar planets is studied by studying the light (e.g., at a particular wavelength) as the planet orbits its star, which is easiest to establish if the planet is a transiting planet, and is easiest to interpret if it is tidally locked, so its rotation is also determined. A spectroscopic phase curve is information gathered by a spectrograph through the planet's orbit, i.e., offering information at a number of specific wavelengths simultaneously. This offers information about albedo, surface hot spots, and atmosphere.