Bytes and the Matrix

Ok, I must admit. I saw the Matrix only once. And that was like two years ago. I know, I am behind the times, but not only with movies. I didn't really know what the numbers were, and how many were considered to be a byte. Eight numbers doesn't seem like it could hold many combinations. Anyway, I also didn't know that bytes were just 1s and 0s. My computer-literate friends tried to describe this to me as we were watching the movie, but I still didn't REALLY get it. Thanks computer class! :)