In Firefox all standalone image pages (for example, when you right-click and choose "View Image"), show their image on a white background. This is good for images that were created with the expectation that they would be viewed on a white background.
However, most people who take care with the images that they create don't make this silly mistake. With this add-on installed, you won't have to see that ugly white background behind your transparent images. Now your images will be rendered against the textured dark grey background, making it easier to see where the transparency starts and begins.
"Access your data for all websites": The add-on checks if each webpage is a standalone image, and if so, it will inject CSS to remove the background of the image. In order to check if each webpage is a standalone image, it needs to "access the data" of the websites. No data is read or stored from the websites. The source code for this addon is free and publicly available at https://github.com/msujaws/transparent-standalone-images