Bandwidth (also referred to as transfer or data transfer by some) is the amount of data your site transfers in a month.
Every file whether it be the web page itself, an image, a download or a video needs to be transferred from the web servers to the computer of the person visiting your site.
When the user connects to your site there is a lot of communication sent backwards and forwards not only asking for files but making the requests for those files. This is what bandwidth is, the amount of data transferred to and from your site.
To draw another parallel it is like your data allowance on your mobile phone.
Our excellent ultra-fast hosting accounts come with unmetered bandwidth, plenty to run most websites.