Binaural and monaural headsets differ only in the number of functioning earpieces: a monaural headset has only one, while a binaural headset has two. However, the term "binaural" carries additional meaning when used outside the realm of headsets.
Headsets are similar to headphones, but they have a built-in microphone. Headsets are common for dictation and transcription. People who work a lot on the phone also usually use headsets, such as customer service representatives.
A monoaural headset includes a microphone and a single earphone. In "The Call Center Dictionary," authors Madeline Bodin and Keith Dawson call monaural headsets "ideal if you want to keep an ear out to what's going on in the rest of the office."
A binaural headset includes a microphone and two earphones. The earphones might be wired to deliver stereo sound, but binaural headsets that are wired for mono sound are common in communications fields.
In other fields, the term "binaural" has a more technical meaning. For example, the phrase binaural hearing refers to the fact that sounds reach our right and left ears at slightly different times, allowing us to spatially localise a sound's source. A binaural recording is one that preserves the listener's localisation ability. Special recording or digital signal processing techniques are needed to make binaural recordings, but any stereo headphones can play them.