To know more about Red Eye and the startling feeling it creates when you see someone with it, one has to understand how cameras work. In all cameras, there is one device called the IRIS which controls the amount of light entering the camera. If there’s more light, more of the underlying film is exposed, if there’s less light, less of the film is exposed.
Similarly, there’s an iris in our eyes which again controls the amount of light entering our eyes. Now, since there are also blood vessels supply blood to the eyes, it’s the blood in the eyes that are caught on film!. This is because the eye has no way to open the IRIS to avoid the problem. To work a way to this problem, most of the cameras now have a Red Eye Reduction mode, where the flash will emit 4-6 flashes(may change from model to model) before the final burst is emitted. This will pre-condition the eye to adjust for the final bright light. This way, the IRIS opens more, so that blood vessels don’t show up in your photo.
To remove the Red Eye, most of the popular softwares already have tools to do so, it’s just point and click.