Bandwidth is the data transfer activity from your web hosting account. E.g. user visits, files transferred.
Most small to medium web site will be covered under most shared hosting bandwidth plans. Unless your website is transferring massive amount of images, video, you should be OK with under a standard shared hosting package. If more bandwidth is required, then go for a VPS/Cloud package with a large bandwidth allocation.
Most top tier web hosts offer unlimited bandwidth, and some place a limit on it.