A phase curve is the brightness of an astronomical body as a function of its phase, e.g., light from the Moon when it is full, half, quarter, new, etc., i.e., phases. Phases correspond to angles of between the direction of view and the direction of the illuminating body. The phase curve can be studied to learn characteristics of the body.
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 it is a transiting planet, and is easiest to interpret if it is tidally locked, so the planet's spin is determined. A spectroscopic phase curve is information gathered by a spectrograph through the planet's orbit, i.e., offering information at more wavelengths simultaneously. This offers information about albedo, surface hot spots, and atmosphere.