Definition and background:
Under the Helmholtz Octave Designation System, a name applied to the octave which extends from middle C (or C 1) below the treble clef staff to B 1 on the treble clef staff. The notes are indicated by lowercase letters with the superscript "1" ( c1, d 1, e 1, f 1, g 1, a 1, and b 1). This octave can also be designated with one hash mark (i.e. C' ) or in the 4th octave under Acoustical Society of America system (i.e. C 4). The MIDI Octave Designation System has two versions, one where note 1 (8.176 Hz) is octave "0" making the One-line octave the fifth octave (i.e. C5), and the other with note 1 (8.176 Hz) at octave "-2" making the One-line octave the third octave (i.e. C3). The indication 8vb (shown below) can be used to represent the same pitches. Typically, this indication ( 8vb) would not be used with the treble clef staff, and since most of the notes in this octave are on the staff, using this designation would not make reading the notes any easier for the performer.
For more information on the music term "One-line" check out these other resources:
Wikipedia - Glossary of Musical Terminology
Virginia Tech Multimedia Music Dictionary
ORB -- Medieval Music Glossary