An extended-range bass is an electric bass guitar with a greater frequency range than a standard-tuned four-string bass guitar.
One way that a bass could be considered 'extended-range' is to utilize a tuning peg that allows for instant re-tuning, such as the popular 'Xtenders' made by Hipshot, however it is more so those bass guitars that have a low-B string such as the five string bass guitar and/or a high C-string - the six string bass guitar - that are most normally considered extended-range bass guitars. Basses have been made with seven, eight, nine, or even fifteen strings with extremely wide necks and custom pickups. These too are considered extended-range basses.
Michael Manring's 'Hyperbass' by Zon guitars and Les Claypool's main Carl Thompson piccolo bass are both four string basses but with necks that exceed the standard 24 frets (24 being the 'standard' for most commercially available bass guitars). Les Claypool's piccolo bass has 32 frets whereas Manring's Hyper Bass is a fretless instrument (however if it were a fretted bass it too would also exceed the 24th fret).
"Extended-range bass" does not refer to bass guitars with double or triple courses of strings such as the eight-string bass guitar or twelve-string bass, both of which could be considered as standard four string basses but with the addition of piccolo bass strings, tuned in octaves. These strings are generally played in unison with the bass strings, thereby producing a natural chorus effect.
The Ibanez Ashula bass guitar, though having six strings, would also not be considered as an extended-range bass because the first four strings - E A D G - lie over a section of the fretboard that has frets whereas the last two strings are - D & G again - lie over a fretless part of the same fretboard.
In 1956 Danelectro introduced their six-string bass (tuned EADGBE, an octave below a six-string guitar). Fender brought out the Fender Bass VI in 1961. In 1965 Fender introduced the first five-string bass guitar, the Fender Bass V.