Bandwidth is the capacity of the network or the server that hosts the website, to send data at a moment. It is the amount of data sent per second from the server. This count more because, if there are many websites in the server and a million hits for the sites the server should be capable of sending that much of data at that moment. If the web server that you host your website has high bandwidth then the users visiting your site would see the pages quickly.

Data transfer is the amount of data that is sent by the server over a period of time. For example the monthly data transfer allowed for a particular site might be 1GB. This means that the website account is allowed to transfer data from their website for only 1GB per month.