A graphic representation of spectrum.
When talking of sounds, a spectrogram is a graphical representation of different frequencies found in the sound. Often, it's grayscale or colored grayscale (sometimes specific kinds of changes of intensities get colored differently); The brighter (or darker, if on light background) the mark on the spectrogram, the more intensely that frequency is present on the sound on that point of time.
Spectrograms of this kind often have two axes, frequency and time. (Typically, horizontal axis has time.)
Spectrograms are most often generated through The Swiss-Army Algorithm Of Signal Processing... Fourier transform. Most often, computer programs use FFT for this purpose.
Often, spectrograms use exponential frequency scale, sometimes logarithmic or linear. The scale in spectrograms often reach from 20 Hz to 20000 Hz (the area of frequencies human ears can hear at best).
Trained eye can identify features of spectrograms easily. Speech researchers can easily tell from speech spectrogram what the subject was saying, for example. When looking at spectrograms of music, drums often show as spikes, cymbals as wide areas. Chiptunes are particularly beautiful - simple synthetic instruments give only narrow lines.
For extremely creative songs that purposefully do wicked things for spectrogram starers, see the "equation" track of Aphex Twin's Windowlicker.
If you want spectrogram programs, for Windows there's a good one available as shareware, simply called Spectrogram, from Visualization Software. For UNIX users, snd is very handy with spectrograms, as is eXtace.
Some people and computer software call this type of things "sonograms", but dictionary.com associates that word more with ultrasound imaging, so I suppose that's an incorrect word in this case...