The style of responding to an e-mail, newsgroup, or forum message with your response beneath the quoted material providing its context, as opposed to top posting, where they are in the opposite order.
Traditionally, bottom posting is done in an interspersed manner, where various parts of the original message are presented followed by the responder's point-by-point reply to each part. Quoted material and new material is distinguished by the use of a prefix character on each quoted line, usually the greater-then sign (>).
Bottom posting is the long-standing traditional method of replying on the Internet, Usenet, and dialup BBSs. Until fairly recently, there wasn't even a term for it, since no other style was known, although (unknown to most of the geek community) top posting was being incubated on various internal corporate networks, for business correspondence, and would eventually be unleashed upon the Internet when the networks became interlinked.
Programs like Lotus Notes and Microsoft Outlook got their formatting cues from the corporate networks used in the markets for which they were aiming, rather than the netiquette of computer-loving academics, techies, and hobbyists, so they were built to favor top posting, spreading that style far and wide to the distress of net oldtimers.
Top vs. bottom posting flamewars break out with great regularity on newsgroups and mailing lists devoted to everything from cats to Harry Potter, and rarely reach any definitive resolution; few people of either style are willing to switch except maybe in a temporary, grudging manner to get along in a particular forum, still insisting that the other way is really better.
Opponents of bottom posting sometimes say that it's bad because you have to scroll down past stuff you've already read to see the reply. This is true only if the person making the reply didn't trim down the quote adequately; generally, one should leave only enough quoted material to provide basic context for the response, rather than trying to preserve the whole long history behind it; usually a paragraph or two is plenty.
Some mail programs, especially the ones from Microsoft, make it very hard to properly bottom-post. On the other hand, Mozilla's mail program has come under some criticism (and a lengthy Bugzilla entry) for not being sufficiently friendly for top posters -- it always places signatures at the very bottom of the message, beneath any quoted material (an opposite problem to that of Microsoft Outlook, which puts the signature above the quote).
A common formatting problem with bottom-posted messages is when the replyer fails to leave a blank line between quoted material and replies; leaving a line that's blank except for a greater-than sign isn't sufficient, because that doesn't set off the quote from the response very well visually, and even worse, sometimes the response gets re-wrapped into the quoted material by a mail reader and the boundary vanishes altogether.