It looks nice, but it's actually a "healthier" way to use your computer, as strange as that sounds. If you use your computer in complete darkness a lot, the sudden drop in luminance from your monitor to the surrounding darkness creates a sharp contrast that your eyes strain to manage.
At the same time as your body wants to close your irises looking at the bright monitor, it wants to open them to view your dark surroundings. By using a bias light, you bridge the contrast between your monitor and it's surrounding and reduce eye strain while keeping your environment relatively dark like you wanted. Since your whole wish is to use a computer in the dark, it's best done with LEDs so that you just get a small amount of light to define the monitor instead of the huge wash that a lamp can cause.
The second benefit is what gives it the name "bias" lighting. The color of the light used behind the display changes how your brain interprets the colors from the display itself. ie, you bias your brain's color interpretation. If you shine an orange light behind the monitor, you perceive everything on-screen as slightly more orange. Same with every bias color, including white.
White will actually make your monitor look better, because the black bezel separating the bias light and your image is now interpreted as a reference black, while the white bias light becomes your reference white. You get a true black and a true white for perfect color balance, which can fake your brain into perceiving a better image than your monitor is actually capable of producing.
The last point about biasing with white LEDs is especially useful for people who edit photos, videos, or want to render realistic 3D scenes for CGI or architecture, because your brain is perceiving more accurate color information. It helps reduce the impact of whatever imperfections your monitor has. In terms of color accuracy, working in the dark is actually better than using desk lamps or fan lights, since those lights are usually warm and cast a warm glow on the display. But that again leads to eye strain, which is solved by bias lighting, which then improves color accuracy even more.