Compression (or more technically Dynamic range compression)is a subtle effect primarily for electric guitar where the highest and lowest points of the sound wave are "limited". This boosts the volume of softer picked notes, while capping the louder ones, giving a more even level of volume. This is frequently used in country music, where fast clean passages can sound uneven unless artificially "squashed".
Compression reduces the height of the signal to a preset level. This level can change over time. Known as 'attack', a greater attack level will give a more aggressive sound.
Another effect of compression is that it expands the length of a held note, or its sustain. The compressor tries to keep the output level approximately the same, even if the input level is decreasing. As a result, the sustain will seem to hold at its original level longer.
Compression has a side effect of raising the background noise of a signal. This can sometimes be circumvented with a properly-configured noise gate patched in before the compressor.
Some famous compressor pedals are the Keeley compressor, The Barber Tone Press, Maxon CP-9 Pro+, MXR Dynacomp, and the BOSS CS-3 Compression Sustainer.