Bandwidth is the amount of data transfer between your website. It should be adequate so anyone who is accessing your website or requesting any other information or processing something should have the access to it. If there is no adequate amount of the bandwidth then it won't work. So monthly bandwidth transfer is the amount of data transfer allowed to your website.
Many hosting provider has monthly bandwidth limit set for the accounts. Once that bandwidth limit is reached then your website will not work. If there is less bandwidth is assigned then website will load very slowly. Visitors will have to wait till the site load. So there might be chances that you would loose your visitors.
You should first check how much daily visitors are there and how much bandwidth is consumed by them.