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Voice compression has a rich history. While today with broadband connections, voice compression is not always required, it is used extensively. As soon as digital transmission of voice emerged algorithms were required to map the human voice into data bits: analog to digital. The telephone system established the base line when it was designed with 64 kilobits per second as a basic voice circuit. As applied in the phone system this standard is known as G.711 which is the designation by the UN body ITU (International Telecommunication Union).
Other G-dot standards compress voice to use ½ or less of the 64K. G.729 is the most popular today, but it is being challenged by newer methods. Historically voice compression was measured by how well it compared to a standard telephone connection, known as toll quality voice. It has been measured subjectively and rated on a scale of 1 - 5, referred to as MOS for Mean Opinion Score.
To further explain voice compression and transmission, you need to consider the audio bandwidth, which is the range of frequencies that are included. As you realize your voice is not as rich when heard over the telephone and this is because of the historical restriction that the phone network placed on audio bandwidth (a whole different discussion). The phone network cannot transmit any audio frequency over 4000 Hz and all of the traditional work focused on that bandwidth as applied to telephony.
The Internet has no restriction on bandwidth for audio, so you see what is happening. The voice quality of Internet transmission can be better than a telephone. Today voice compression algorithms account for the greater audio bandwidth and so can deliver much better sound than telephone-based approaches.