When shopping for a new headset, you'll find they come in two varieties: monaural and binaural. While these words sound impressive, they really only refer to the number of earpieces in the headset's design. The differences between the headsets themselves, however, make them well-suited to different environments and uses.
Monaural headsets consist of a single earpiece and a microphone. These headsets are generally better suited to environments where you need to be aware of what's going on around you. A good example is in a call center, where an operator needs not only to be able to hear the customers on the phone, but also his co-workers. Designs vary, but these are typically lightweight for ease of use. Full over-the-ear earpieces are less common than single earbuds or a small speaker.
Binaural headsets include a full pair of headphones and a microphone. These headsets are optimal when you need to focus on the conversation itself and drown out surrounding environmental noise. An example would be during an online gaming session, where a player needs to hear her team-mates and the in-game audio, but would find anything going on in the room distracting. Like monaural headsets, designs vary considerably. Over-the-ear binaural headsets are more common, including models that feature noise-cancellation, simulated surround sound and other premium features to enhance your experience.