Basically, top posting is when you reply to a post/e-mail/etc by quoting the entire thing, with your response on top. It's annoying, can be difficult to understand, and considered improper netiquette.
Bottom posting is where you go through the document you're responding to, and trim out what isn't relevant, placing your responses under each quoted section as appropriate. It adds context to your reply, making it much easier to read and understand. And, by removing the unnecessary parts of the original document, you're reducing the bandwidth and disk space required.
Many people these days do top posting, because certain crappy e-mail programs (specifically Outlook and Outlook Express, though they are by *no* means the only culprits) default to placing the cursor at the top of a response e-mail, while quoting the entire original message below it. Today I came across one of the best quotes I've seen for why that alone is not a good reason to 'top post'.
Posting at the top because that's where the cursor happened to be is like shitting in your pants because that's where your asshole happened to be.
I think that about sums it up.