The images taken by the Hubble Space Telescope are in black and white, but each image only captures a certain wavelength (color) of light.
The Guardian has an excellent video that explains how the images from the Hubble Space Telescope are created.
Each image from most research telescopes only capture certain, specific colors (wavelengths of light). One camera might only capture red light, another blue, and another green. These are captured in black and white, with black indicating no light and white the full intensity of light at that wavelength. Since red, blue and green are the primary colors, they can be mixed to compose the spectacular images of stars, galaxies, and the universe that NASA puts out every day.
Three galaxies. This image is a computer composite that combines the different individual colors taken by the telescope's cameras. Image from the Hubble Space Telescope via NASA.
The process looks something like this:
How images are assembled. Note that the original images don't have to be red, blue and green. They're often other wavelengths of light, like ultra-violet and infra-red, that are not visible to the eye but are common in space. So the images that you see from NASA are not necessarily what these things would look like if you could see them with the naked eye.
