Broadband speeds define how fast data can be transferred down your telephone line.
Some examples
If you want to download a 35-page Microsoft Word report or PDF, which is 500Kb (half a Megabyte) in size, it would take about 1-2 minutes on a dial-up connection and just half a second on an 8Mb connection.
If you wanted to download an episode of Lost or 24 from Sky, with an hour-long episode measuring 400Mb, it would take approximately half an hour over a 8Mb broadband, and 17-20 hours using a 56k modem.