[This explanation courtesy of Binkmeister.]
"Bandwidth" refers to how much digital traffic a given website (or server) can use at any given instant. Another term that is used is "pipe" which is a decent metaphor.
Think of a water pipe in your bathroom. It takes water from a main pipe beneath the floor and runs it to your faucet, and is about half an inch to 3/4" in diameter. It can push a certain amount of water through it at one time. (To keep this metaphor working, assume the water pressure is always constant.)
Turn on the faucet, water comes out. Now, think about that pipe under the faucet being twice the diameter. Suddenly you've got four times as much water coming out. Bigger pipe = more coming out of the pipe at a time.
Same with the Internet and websites. The wire that comes out of a web server is just like that pipe in your bathroom. The bigger the pipe, the more water (or information) can come out at once. And just like your water main at home, the web server pipeline is measured to find out how much goes through it. And just like the water company, the Internet Service Provider for BZ charges for how much goes through a pipe.
Now, to translate that for BZ: each post (including this longwinded one that nobody will finish reading) takes up a certain number of "bytes," which is how information is measured in computers. Think of a byte as a drop of water. Each character you see on the screen (and the code that formats it) is about 1 byte each. Images take up a lot more bytes than text, kilobytes (KB) or megabytes (MB). This post would be about a cup of water, then. And every time someone loads this page, it's like turning on the faucet... and somebody pays for it. In this case, D.
Of course, it takes a LOT of cups of bytes to serve up BZ, and the ISP is an understanding and generous host. But every byte that goes out of the server is counted toward the total. If there are wasted bytes, it still needs to be paid for.
So, treat BZ as if it were your own home... turn off lights when you leave a room, don't run the water unnecessarily, don't post spam, don't link your avatar or sig image from within a post, don't post meaningless gibberish, etc.