Think of the internet as a big library. I can find anything in the library if I know where it's located. The same is true of the internet. To find something, I have to know it's location. That's where its URL comes in. Everything on the internet can be identified by its URL - it's Uniform Resource Locator.
Now let's say that I find an image on your website that I like. I can copy the URL for the picture onto my website, and people can now see your picture on my site, too. They don't see a copy of your picture; they actually see your picture through a direct link.
That's a hotlink.
It takes bandwidth to display anything on the internet, including images. When I hotlink to your image, I am using your bandwidth to show your image on my page. It costs you money. It's like plugging my t.v. into your electrical outlet without paying you for it.
Here's where the plot thickens. Let's say I gather up all the images that I find on the web that I like. I make them available for you to use. I have a "free use" site; I don't charge you anything to use the pictures that I collected.You're happy, I'm happy. But Stan is furious. Stan is the guy whose site I got the picture from that you're now using. Because you are using his bandwidth, he has less for his own use. And he is paying for the bandwidth you are using.
So I'm making a better effort to avoid hotlinking, and you may want to, too.
When you use just the URL of an image (copy and paste the url), you connect directly to somebody else's server. Instead, copy any image and upload it from your own computer, or use images from an image hosting site that provide a new internet address for the image you post, like this one for the picture below: http://i63.tinypic.com/14dpymc.jpg
A few good examples are Photobucket, Flickr, Imgur, and smugmug. Most of these have a free or low cost membership option. There is also a great little site called tinypic, where you can generate an http address from an existing URL.
I hope this is helpful. If you have any questions or if you can help me say it better, please let me know.