Monthly bandwith is just the total volume of data transfers out of your site in the course of a month.
Suppose that your site consists of mainly text pages that average 20k bytes then, if you serve 5000 pageviews a day that's 100MBytes a day or 3GB/month.
If you serve images, video or mp3 data, you can use a lot more bandwidth very easily.
You should be very cautious about exceeding bandwidth allowances. You might find that you get cut off but, worse, you might find that you are subject to very high charges. Look in the ISP's T&C for nasty clauses. There was a piece on wired news a while back about a kid who captured a demo ad for a new game and put the resulting file (tens of megabytes) on his web site. It was a big hit with his fellow gamers and his host just transferred all the traffic for him and then hit him with a bill. Fully in line with his traffic and their published Terms, they billed him for a few tens of thousands of dollars.
There are also reports floating around of some disreputable hosts using this as a sort of legal con. You set up a host service with very attractive prices but burried in the small print is a very low limit for bandwidth (just a few megs a month) and a high charge for exceeding the limit. You go over the limit and suddenly find that your credit card has been billed for several hundred bucks. Ouch, it's nasty and devious but what can you do? You agreed to the terms. (I think that there was something about this on wired too.)
Hope that helps.
jpoc