What does a "blown-out background" mean in photography?

"Blown out" means the maximum value for all color channels.

For RGB, that means maximum red, maximum blue, and maximum green. This appears to be pure white, even if the color of the subject is not white or a shade of gray.

If you take a baby blue wall and expose it properly, in the resulting image the wall will be baby blue. If you over expose it enough, though, even the green and red channels will reach full saturation and it will look white in the resulting image.

This is because there is only so much red that the red channel can record as a numerical value, so much green that the green channel can record as a numerical value, and so much blue that the blue channel can record as a numerical value.

Imagine the image is grossly overexposed and there's enough green light to give a value of, say, 10,000, but only enough blue and red light to give them comparative values of 320 and 442, respectively. If the maximum value for each color channel is 255 (8-bit raster image format), then all three color channels will have a value of 255 (255,255,255) because that is the highest number each channel can record in 8-bits. Since all three channels are at their maximum values, and all three channels are at the same value, the resulting color when viewed will be pure white.

Now apply this to a photo of an interior room with windows during daylight hours. The room is a lot darker than the outdoors seen through the windows. If we expose properly for the room, the widows will show up as pure white squares and no details of the world outside will be recorded in our photo. On the other hand, if we expose properly for the world outside the windows, the interior room will be almost pure black (0,0,0) with details lost in the noise floor of our camera's sensor.

For examples of how this can work out in different types of photography, please see:

Why is it that when the green channel clips, it turns into blue?
Why is my long exposure shot all white?
How to photograph a room showing both room & view out a window?
How many lumens are required to achieve a pure white background in a 40cmx40cm softbox?