Dial up internet had a few drawbacks that would eventually find people dumping it for faster internet connections that wouldn't tie up your phone line, cost you a local call when you wanted to connect, would download webpages, emails etc alot faster and would offer a lot more flexability when it came to networking and being able to travel and access the internet at the same time. The new types of connection were then referred to as Broadband as the connection was a faster (the bandwidth was larger) speed.
Broadband is basically a marketing term and there are a few types of internet connections that fall into the "Marketing Term" Broadband.
ADSL - This type of internet connection uses an ADSL modem which connects to your phone line, downloads anywhere from 6 - 400 times faster than dial up but doesnt tie up your phone line, allowing you to make and receive calls while accessing the internet. There are many providers who offer ADSL and a few different speeds available. The two types of ADSL are ADSL 1 and ADSL 2+. Make sure to shop around if your looking into getting an ADSL or ADSL 2+ connection as dfifferent providers will offer different speeds at different prices which you will be amazed at how much they varie.
Cable Internet - This type of connection is only available in areas which have dedicated cabling installed. This type of connection uses a dedicated cable from the street, only provided by Telstra or Optus which doesnt need a phone line at all and downloads at speeds similar to those of ADSL.
Mobile Broadband or Wireless Mobile Broadband - This internet connection uses the mobile phone network and can be used anywhere you get mobile coverage or where your provider provides you coverage. There are a few providers you can choose from which offer different coverage areas as well as different prices, so once again shop around and ask about both coverage and price. This type of connection can be expensive and vary alot in sopeed, I would only recommend this as a secondary internet connection if you need the internet on the road or when cable or ADSL is not available.
There are other types of internet connections that are used but these are the most common types that are in use today in both Home and Businesses. When choosing a type of internet connection make sure to look at all your options and to find exactly what sort of speeds you will be getting, what sort of download limit and how much it will cost.