I believe the speaker phone was the first foray into hands free cell phone communication. The hand set had a microphone and a loud speaker in it which enable two things to happen. One was that it freed up the hands to drop the phone and do other things. The second thing was that it enabled multiple people to be heard in the conversation.
The next i believe is the mobile phone headset. It is a cable connected to the phone with a single earphone and a microphone. They are usually designed as ear buds or over-the-head devices. They are connected to the phone with a wire and as such do not give you that much range of freedom from your cell phone. They can be used to play music stored on the cell phone as well as provide freedom for your hands.
Most users however are moving to the wireless hands free devices. Blue tooth devices do not use cables but exchange information through short-length radio waves. They connect devices and exchange information between these devices such as mobile phones, laptops, video game consoles and other devices. They make use of little power and communicate through transceiver microchips in each device. Communication is only possible when both devices are in range. These devices are used basically to talk with people without holding the hand set but they also transfer files in byte data.