Broadband is high speed Internet. It means that you are getting a faster connection and things work quicker for you on the Internet. Some things like watching videos or games require broadband for it to work well.
The definition of broadband recently changed. It used to mean that you had a download speed of 4 mbps (megabits per second (mega means one million and a bit is a single binary digit, it takes 8 to represent a character usually) or faster. Recently the FCC redefined broadband to be 25 mbps or faster. This change means that DSL (faster internet thru the phone system) as we currently have in the USA is no longer defined as broadband as it works up to 6 mbps. However there are new ways to do DSL (with new equipment for telephone companies and consumers that will allow much faster speeds).
Cable speeds vary widely by location by many places are starting to offer 100mbps to 1 gbps (think Google Internet in some places and EPB in Chattanooga) and even 10 gbps (EPB starting to offer in Chattanooga. gbps is gigabits per second and giga is one billion, so 1 gbps is 10 times faster than 100 mbps. Dialup works up to a speed of 56kbps or kilobits per second and kilo is 1000. In all three cases the numbers I gave are round numbers, the actual is a number very close but uses more of the digits, so most people round to thousand, million or billion.
As a result of the change in definition, a lot of areas in south Georgia that had finally begun making broadband available thru DSL discovered they no longer offer broadband. North Georgia and southeast Tennessee still have a large coverage of broadband.