Bandwidth is the amount of data that is allowed to be transferred in and out of an account during any given period (usually 1 month) in either MB or GB. For instance, if a client has a 1MB picture stored on their server and that picture is accessed 4 times, then 4MB of bandwidth has been used.
This is the amount of actual data that can be transferred from the web server that holds your website, to the browser of the person who is looking at your website. If you go over the limit, then either you will have to be billed an extra fee, or your website will not be available. The amount of bandwidth you use is obviously related to the amount of traffic (visitors) that you receive.
Unlimited bandwidth offered by other web hosting companies sounds like a good deal. This is not only impossible, but would cost an unlimited amount of money to the web hosting company. The moment you try to use a lot of bandwidth – you might find your website shutdown or a request for you to upgrade.
For most web sites you will not need much bandwidth. Probably 99% of all websites use less than 5 GB of bandwidth a month. If you intend to have a lot of downloads of software, audio or video, then you may end up using a lot more bandwidth, maybe 50 GB. Sites like mp3.com require an enormous amount of bandwidth, but for the average site – a low level will be enough in almost all cases to start off with.