They are designed for deep, wideband photometry (with high spatial resolution thanks to Herschel's large 3.5 meter mirror) and full spectral coverage, making Herschel the first space facility to completely cover the far infrared and submillimeter range. Together, PACS and SPIRE are capable of detecting light from 57-670 microns in wavelength. HIFI covers 480-1250 and 1410-1910 GHz (which corresponds to about 157-625 microns).
The three instruments are designed to compliment each other. SPIRE and PACS have imaging spectrometers that provide spatial information, while HIFI resolves with very high spectral resolution, but only one line at a time and in only one beam on the sky.
The emission lines of the main interstellar cooling agents are predominantly in the PACS range, but fall into the SPIRE wavelength range for very distant and hence highly redshifted objects. The combination of both instruments will provide the full range of information needed to determine SEDs (spectral energy distributions - the total amount of power radiated by cosmic objects, measured in watts), photometric redshifts, total luminosity, and accurate positions.
SPIRE and PACS will both conduct deep surveys with their photometers to find galaxies from the early Universe, and follow up with spectroscopic studies of the most interesting objects.
Observing light in that range means that Herschel will detect subtle "heat" emissions from very cold objects, such as vast clouds of interstellar dust. The spacecraft has to keep its instruments cold because their electronics work only at frigid temperatures, and to prevent the instruments' own infrared radiation from drowning out the faint signals they're trying to detect.