Hi, I'm the owner of AstroBin and I found this thread with a Google search. I'm happy to help.
As it's been said,
hotlinking means to post a
direct link to the JPG/PNG/GIF file, by right-clicking on the image and choosing "Copy image URL".
I discourage that because it takes bandwidth from AstroBin (which I pay for), but people will not see that the image comes from AstroBin, and don't get a chance to know how great a website it is. :-)
The proper way to share is through the "Share" menu, where you can select the Simple, Forum, or HTML modes. That gives you a link that is good to share wherever you want, and points to the AstroBin page that contains your image and all the technical details you associated with it, the comments and so on.
For instance, this is an image of mine:
http://astrob.in/19455/
If you have any questions, don't hesitate to reach me via the Contact form in the Help menu, and if you haven't already, read the Help and FAQ pages! :-)
http://www.astrobin.com/help/
http://www.astrobin.com/faq/
PS: Thanks JJJ for spreading my work :-P
Salvatore Iovene.