In reply to mypyrex:
No it's the amount of data sent from your site to visitors' browsers, so text, images, videos, etc. Each time someone views a page all the bytes transferred are added up.
Without knowing what your ISP's terms are - it sounds like you are using one of the free webspace accounts that ISPs bundle with their deals then it's a choice between upgrading your account with them or moving the data on the webspace to another provider. Other than people losing bookmarks there's not a lot of pain involved. Yes, you'll have to pay, but a lot of web hosting plans are pretty low cost in the scheme of things. Also if you do switch then you'll be offered things like your own domain name (assuming you don't have one already), OK, basically they're inducements.
If you don't want to switch then look at the sizes of all the files on your site, it will usually be the case that videos are the largest files, followed by images then plain text (html) files. If you have any Flash on your site then that will be pretty big as well. If you have access to the server logs or have Google analytics installed on your site then you'll be able to see the most popular pages and therefore what's contributing most to your bandwidth. Use this info to put that content on a CDN. What you do is rather than host the files on your site, i.e. on your ISP's servers, you put them on different servers and link to them. You can use Google Drive to do this
http://blogvkp.com/using-google-drive-as-cdn/ and probably Skydrive and iCloud as well. Your visitors see the same site, it's just that it comes from two different locations. Obviously there are potential problems with this as well.
HTH
ALC