, a device used to extend the range of a double bass
The extension is one of several solutions to a problem of most (classical, that is orchestra/Symphony) double bassists, namely that composers require them to play notes deeper than contra E, the normal bottom limit of the instrument.
In the past, this problem was sought alleviated by different tunings, and different numbers of strings on the instruments. Today, there are two choices if one wants to play those really deep notes. One is to play a five string bass, which is hard, cumbersome and just plain difficult. The other is to have an extension fitted to your instrument.
An extension is a device which lengthens the fingerboard (sic!) of the deepest string (tuned normally to E), thus making it a C string. 8)
Extensions come in two kinds: mechanical and fingered. A mechanical extension uses a complex array of springs and levers to press the string down, enabling you to play the notes between E and C. The fingered lets you do the work yourself, but also gives you more control. This can help intonation, sound and speed of playing.
An extension is generally a Good Thing.