The telephone network allows data traffic between two points at a rates around 10-40 Kbit/s. Some recent advances in the compression of audio and video allows the use even of telephone lines for applications such as ``call-for-a-radio-program'' with a reasonable quality. Much of the personal Internet access occurs using a normal telephone line closest to the terminal (personal computer).
The current cables allow for digital transmissions to the customer of up to 1 Mbit/s. You can lease digital lines to achieve this speed (or more) for point to point connections.