Ok well if you access the internet using a modem (modulator-demodulator) then when you send/receive data, then what is actually happening is the modem turns the data into (modulated) sound... squeaks beeps, crackles etc (you can hear it if you pick up another phone whilst connected). This is as opposed to using the actual telephone line itself to transmit the data. Broadband connections involve using your telephone line as a direct data connection rather than sending data as sound, as modulated sound only has a limited maximum speed.
As to why it is so expensive, well, partly because the BT telecoms infrastructure is very poor, so they may need to upgrade part of their stuff in your house.
Also you may need an ASDL modem or other such routing equipment.
There is of course a lot more to it than that but thats it in a nutshell.