The term broadband is used to cover two main technologies in common usage at the current time: and these are described in the sections below.
Asymmetric Digital Subscriber Line (ADSL) is a type of DSL. It works by splitting an existing telephone line signal into two, one for voice and the other for data. ADSL technology can work at up to 8Mbps download. The most popular services in the UK at the moment are running at speeds of 512Kbps (approx. 9 times faster than a modem), although speeds of up to 2Mbps can be obtained. Upload speeds are 256Kbps on all products and hence this is why it is "asymmetric", because the download speed is different to the upload speed.
To summarise therefore, ADSL is a type of DSL where the upstream and downstream speeds differ (hence the "asymmetric" part). There are many variations of DSL technology for different types of application (HDSL, SDSL, etc).
The second major broadband technology commonly available is Cable. Typically cable providers will provide not only an internet connection but also telephone and televison services on the same cable. Examples of such providers, in the UK, are NTL and Telewest.