On forums like this one, you can upload pictures directly to the forum from your computer and they won't vanish.
Other forums don't want to use their storage space to store zillions of bits of photo data so they are set up to only show pictures that are stored on another web site like Photobucket or Flickr or whatever.
This saves the forum a lot of space which can be used to store great topics like this one.
The reason it saves a lot of space is because, when the forum computer sees a photo link in your post it just goes out on the web and temporary calls up the data from the storage site and then shows it like it is really there.
When you leave the topic, the temporary picture data is forgotten by the forums computer leaving memory available for other stuff.
A person can get their own "web site" and store their pictures there.
If they do this, they can link the pictures on their web site in their posts on those other forums that don't offer to upload pictures and the pictures will show up as long as their own web site is operating.
I don't know the fine points but a man I have great faith in when it comes to computer stuff on the web said while speaking about uploading your pictures to your own site, "You would need to learn a little about uploading the files (via FTP)", whatever that is.
GoDaddy will set up a web site for you for about $12 for the first year and $100 per year to keep it going.
With your own web site you can post just about anything you want to and you are in total command.