A comma pump is a harmonic sequence (or chord progression) wherein the tuning base shifts up or down by one comma. This means that in JI, the chord prgression would not return to the original starting pitch, but a different pitch that is a comma off. If the chord progression is repeated many times, the tuning will steadily rise or fall (and also an unlimited number of different pitches would be required).
If, on the other hand, the chord progression is played in a temperament in which the comma vanishes, it does return to exactly the same starting pitch. This means that comma pumps are very characteristic chord progressions of a particular temperament family. For example, Western classical and popular music is in meantone or 12edo, which tempers out 81/80, and accordingly 81/80 comma pumps are very familiar chord progressions. Comma pumps corresponding to other commas of 12edo, for example 128/125 or 225/224, may form the basis of interesting chord progressions in jazz or other 12edo music.
For other examples of comma pumps, see Comma pump examples.