I can answer this.
When you attach photos on this forum, you would upload it from your computer to the server that runs the forum. You would see a window pop with "My Computer" (which is indeed YOUR computer) and you would have to click on the right folder and file name that represents the picture you want to upload.
At that point, it is stored on the forum for others to either look at or download. In other words, once you attach the picture ( don't see that you have actually done that?), they are not being pulled by your computer any longer. That only occurs once when you upload it.
After the picture has been uploaded, when someone, or you, click on the image itself once it was been posted, it should expand and "blow up" so to speak for easier viewing of the picture.
When someone, or you, click on the paperclip or the blue image file named (ending in .jpg), it DOWNLOADS the picture from the forum to your computer (or whoever's computer clicked it). It should appear in "My Downloads" (for Windows) or "Downloads" on a MAC (or whatever folder you have designated to store files that are downloaded from the internet). Or it might bring up a window that asks you where you want to download it to, depending on your windows version and how it was setup.
The act of clicking on the paperwork, or the filename.jpg (AFTER it was uploaded already) is so you can save someone else's picture on your computer. Again, you are pulling the picture from the forum at that point. So is everyone else.
You are in NO DANGER to anyone accessing your computer. Think of it like you uploaded it to the cloud and others are pulling it from the cloud.
Let me know if you have any questions.