I asked this before, WHY do we need a place like IMGUR or Pbucket anyway?
On this particular forum you don't. TTR can function as it's own image host. This means that the Xenforo software allows you to create image links that let you embed images. Also, when TTR was set up, additional space was anticipated to provide storage for us to upload images.
Traditionally, however, forums and their predecessors, bulletin boards, were essentially text-based platforms with very little native image capacity. Storing text on a server consumes very little space. Images consume much more. In the past, storage was more costly and server space was more limited.
In order to embed images into a forum, you have to link to another web location. This is where sites like Photobucket come into play. They provide storage for photos. In reality, whether you put the images onto TTR or someplace like Photobucket, the process is the same...an image is linked in the post. The only difference is where your browser goes to display the image...on TTR's own server or some other location.
Now, you may wonder why Photobucket would want to charge for linking if storage is actually less expensive. The real cost is not in the price of a hard drive. Think of it...every whenever someone pulls up a page that has an image you've posted, their browser navigates to the web address where that image is hosted and displays it on your computer. It actually retrieves the image and stores it in your browser's cache. Now, think of all the people around the world who may do that. The hosting server is dealing with a lot of image requests and has to serve those back to the requesting computer. Not only does that put the server through a bit of a workout, but it requires bandwidth to meet the demands of all the people. This does not come free. There are real servers housed in real buildings that require a lot of power and climate control and real IT technicians to keep it all running. There are a multitude of other costs, as well.
Incidentally, this is one of the benefits of having a browser cache. If, during the same browser session, you revisit the same webpage, in most cases, if your browser encounters a link to the same image you've just seen, it will display the image from the cache rather than making a fresh request back to the image host.
My issue with Photobucket is not so much in wanting to be paid. I suspect all the free hosting services will eventually have no choice but to charge something, as well. Ad-driven revenue streams only go so far. My problem with Photobucket is with how they rolled this out. I also think the huge price they want will really hurt them. I think they'd have gotten better reception if they charged a much lower price. More people would have stuck with them and begun paying. Not only are they losing the free account holders, but they've alienated those who were actually paying, but at a lower pricing tier.