How Magnet Links Are Different From .Torrent Files
When you download a .torrent file, you're essentially downloading a small file that contains information on the larger files you want to download. The torrent file tells your torrent client the names of the files being shared, a URL for the tracker, and more. Your torrent client then calculates a hash code, which is a unique code that only that torrent has—kind of like an ISBN or catalog number. From there, it can use that code to find others uploading those files, so you can download them from them.
A magnet link does away with the middleman. A magnet link is essentially a hyperlink containing the hash code for that torrent, which your torrent client can immediately use to start finding people sharing those files. Magnet links don't require a tracker, nor does it require you to download a separate file before starting the download, which is convenient.
How to Use Magnet Links
Magnet links are dead simple to use. If you head to the Pirate Bay now, you'll notice that magnet links are now the default, with the "Get Torrent File" link in parentheses next to it (a link which will disappear in a month or so). Just click on the magnet link, and your browser should automatically open up your default BitTorrent client and start downloading. It's that easy.
What This Ultimately Means for You
The short answer is nothing. In fact, it could mean that downloading torrents takes one or two fewer clicks since all you have to do is click on the link to start the download. When magnet links first came out, not all torrent clients supported them, but now you can use magnet links with just about any semi-popular torrent client out there.
The main reason torrent sites are moving toward magnet links—apart from convenience to the user—is that these links (probably) free torrent sites like The Pirate Bay from legal trouble. Since The Pirate Bay won't be hosting files that link to copyrighted content—that is, the torrent files—it's more difficult to claim the site is directly enabling the downloading of the copyrighted material. Whether this semantic leap actually protects torrent sites remains to be seen, but for now, you can sleep soundly knowing that the sites will stick around for a while longer and that your torrents will take one less click to get started. If you want to read more about magnet links, check out the Wikipedia page on the subject.