Hotlinking is when you copy and paste the source of a media file (direct linking), and post it to your site or blog. It's bad because it piggybacks the responsibility of bandwidth to someone else.
This is considered bad form because it steals bandwidth from the host. Bandwidth costs money, so you cost the host money. Your action might also cause the host's site to crash, which is also really terrible. So if there's a media file you want to use (and it's fair use or you have permission), you'll have to save the file yourself and upload it to a server yourself. You can use your own server or site, or a site like Flickr or Photobucket. Luckily, some sites will provide a link you can use or an embed code, which might lessen the time required to uploading the file yourself.
Don't forget to credit the file's source, and be sure you link to the site where it originated!
You can end up at the end of a prank if you hotlink, which is another reason to be wary. (But breaking the code of the Internet is reason enough.) This happened to John McCain's MySpace in 2007, and National Organization for Marriage earlier this year when it hotlinked from a web comic. (That both examples oppose gay marriage is purely coincidental, though I support both pranks. And that last link is especially insightful. It also explains wanging.)
So lesson learned, Old People. Host your own media. It's the polite, and safe, thing to do.
Hotlinking is also called leeching, piggy-backing, direct linking, and offsite grabbing.
Hotlinking: What Is It, And Why Is It Bad?, Squidoo
What Is A Hot Link? wiseGeek
Inline linking, Wikipedia
John McCain's MySpace Page "Enhanced", Tech Crunch
N.O.M. N.O.M. N.O.M., The Weinerworks