Various definitions of "bandwidth"
Bandwidth refers to the capacity of a communications line/channel to transmit/receive information and is measured in bits, bytes, kilobytes, megabytes and gigabytes.
Internet Service Providers
Bandwidth (when specified by an ISP) is the monthly quota of data that you are allowed to upload and download with your internet connection, your monthly bandwidth allowance will (usually) be measured in Megabytes or Gigabytes, the amount of bandwidth you need depends on how you intend to use the internet.
For example, if you will be using the internet just to view websites, then you won't need as much bandwidth as someone who is downloading music and video for the same amount of hours.
note: one Megabyte (MB) = 1024 Kilobytes (KB).
* The average webpage is around 50KB (kilobytes) including images
* The average MP3 audio file is around 4MB (Megabyte)
So you would use the same amount of bandwidth to download one MP3 audio file as you would to view eighty one webpages (50Kb) on the internet.
As you can see it depends greatly on what you are using your internet connection for as to how much bandwidth you will need.
Web Hosting companies
When in the context of web hosting companies it refers to how much traffic a web hosting company will allow each month.