Dial-up connection can be initiated by your computer modem. The connection is established and maintained in a limited time duration. Usually dial-up connections only has a 56kbps speed. In Dial-up connection, you have to connect first before you can access the internet.
A broadband connection usually is like our cable tv. It doesn't require telephone lines to connect. It has a much faster speed compared to dialup connection. Most of broadbands uses a optical wireless media. You don't have to connect, when you open you computer, automatically you are connected to the internet.