Hotlinking, also called direct linking or bandwidth theft, means using the URL of an image on someone else's server or hosting account. Instead of saving the image to your own computer and then uploading it to your own hosting account (such as Photobucket, for example), you simply check the properties of the image and use the URL being used to display the image.
Hotlinking is bad because it often costs people money. Most people have a certain limit on their bandwidth, or data transfer, for each month. This data transfer occurs every time someone views an image, a webpage, or downloads a file from the hosting account. When you use someone else's image without uploading it to your own host, you are using up the other person's bandwidth. If the person goes over their limit, two things can happen:
1)Their account can be shut down for the rest of the month. If they use an image host this may simply mean they won't be able to post their images anywhere until the new month begins. If they own a website, this will mean that nobody will be able to view anything on their website, not even web pages, until the new month begins.
2)They can be charged overage fees, just like on a cell phone, and these fees usually are not cheap.
Note that hotlinking is also bad because you have no control over the image you are displaying. If someone discovers you are hotlinking from them, they might just remove the image or change its URL so that you get little red X's in place of the image. Or they may replace the image with a banner that says something like "I'm a stupid hotlinker - I steal bandwidth from so-and-so." Or they may get really annoyed and replace the image with something disgusting or inappropriate (I doubt you'd want to go to your journal and see [insert porn or something that disgusts you here] as your background).
If you need help finding an image host, feel free to ask in the community. You may also want to read the LJ FAQ about remote loading.
Edited Oct. 30, 2005 - apparently God/the powers that be/the almighty three-headed llama that rules us all demands that LJ be politically correct at all times.