When light is passed through a prism or a diffraction grating, it gets separated out into its constituent colors. The resulting pattern of colors is called a spectrum, and a great deal of information can be gleaned from these spectra. For many sources of light like the sun, or a light bulb the spectrum appears as a continuous range of colors, from red to blue (for the optical wavelengths; all of this can be extended to wavelengths beyond human vision, of course), while for thin clouds of gas (such as those we are looking at) we get a discrete spectrum, due to the quantized nature of atomic energy levels.
On spectrum above, the vertical (up/down) axis represents the spatial axis along the slit. Going up and down corresponds to going left and right along the slit shown below. The horizontal axis respresents the wavelength dispersion with shorter wavelength (bluer) on the left and longer wavelenth (redder) on the right.
Looking at known spectral lines (researched in great depth in labs here on Earth) from the distant galaxies, we can determine several things right away. One of these is red-shift (a shift in the wavelength due to relative motion of emitter and observer), which in turn gives velocity and even a rough idea of distance. Our research went even further, and uses the relative strengths of different lines to determine such physically interesting quantities as temperature, density, extinction (extinction is the amount that light gets scattered or absorbed between the source and our instruments; this may be due to the atmosphere or extraterrestrial factors and it can affect different wavelengths differently). For stars, we usually just get the spectra of a point, so there is one dimension in the spectrum, that of wavelength. But in our case, we wanted a cross-section of the galaxy, so we used a long, narrow slit (hence ³long-slit spectrum²). This provided a second dimension in our spectra, a spatial direction.
This slit could be oriented in various directions to facilitate the study of a maximum number of HII regions in the various galaxies.