Hotlinking, inline linking, remote linking and many other terms are used to describe a way taking images, or other files and embedding it directly into a website. In other words, you are using their bandwidth illegally. Hotlinked files are files not stored on your own server.
There have been several reports across the English section of AAO of hotlinking, especially in trials. Hotlinking is generally forbidden and most sites will have a note saying not to hotlink.
"But what if I need Image X?"
The answer is simple.
Download it to your hard drive and upload it to a web/image server that allows hotlinking. Websites that allow you to do this without being banned include Imageshack, Photobucket, Fileden and more.
By doing this, you don't waste the bandwidth of another site. The servers you will use instead are specifically designed for these purposes so you don't need to worry about breaking any rules.
If you need any more information or are still confused, then either post in this thread or check out the links below!