In order for the camera and lens to create a proper exposure, a certain amount of light needs to hit the film plane or sensor. Not only is a large maximum aperture useful for controlling depth of field, it also allows the lens to gather more light. Using a larger aperture setting results in a faster shutter speed (time the lens aperture is open) for obtaining a proper exposure.
When shooting in low light using a zoom lens with a maximum aperture setting of f/3.5 or f/5.6, the resulting slower shutter speed often produces blurry pictures. In these situations, the larger maximum aperture of a 50mm prime lens would allow for use of a faster shutter speed to minimize blurry pictures from camera shake.
The sample pictures below show the usefulness of a 50mm prime lens in low light situations. Both images were taken with a 50mm prime lens at an aperture of f/1.8.

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