Unfortunately, humans can only see light from a very small part of the electromagnetic spectrum. Quite literally, there is a whole universe out there that we can't see. Fortunately, we have technology to aid us.
This fantastic image of the Sun shows us how our star looks from the visible part of the spectrum to the extreme reaches of the ultraviolet wavelengths. Of course, the light received by our observatories had to be translated into a color that we could see, so this isn't *actually* what ultraviolet light looks like; however, the image does give us a pretty good idea of how much of our the Sun we can't see.
This image was compiled using image data from the orbiting Solar Dynamics Observatory(SDO). The base of the image (the orange part on either side, shows the Sun at visible wavelengths. The wedge-shaped segments show the solar disk at increasingly shorter ultraviolet and extreme ultraviolet wavelengths. As you can clearly see from these images, at the shorter ultraviolet wavelengths, a lot more detail seems to be revealed.
From our perspective on Earth, if you observe the Sun it appears yellow and, sometimes, a little reddish. The yellowish appearance of the sun is mainly caused by the way that the atmosphere scatters blue light. Also, yellow is the brightest wavelength the Sun emits that can be seen with the naked eye, but of course, the Sun emits light in all wavelengths. While we can learn a lot about the sun by observing it in the visible spectrum, we can greatly expand on that knowledge by observing different wavelengths that are invisible to the human eye. By building specialized telescopes, we can learn about the sun’s composition, activity, and keep a closer eye on the Sun. Ultimately, this allows us to be better prepared for whatever the sun throws at us.
To learn more, see this article on the Sun's wavelengths and what they tell us.