(from an article in the January-March 2015 EOS Magazine)
Using a Speedlite as a creative light gives a new depth to images. With a Speedlite on the camera hotshoe, or the built-in flash, the angle that the light hits the subject is flat and the result is often quite stark. Moving the Speedlite off the camera hotshoe allows a photographer to position the light to create shadows that give depth and texture to pictures.
On-camera flash aimed directly at the subject often creates unflattering red-eye in human subjects, and green-eye in cats and other animals. Using an off-camera flash will usually eliminate this.
A single Speedlite flash on the camera is a small sized light source. Softer more flattering light is created by comparatively larger light sources, though there is a physical limit to the size of diffuser for on-camera flash. It is not just the softening effect, but also the direction of the light that is important. Light from the side creates shadows and highlights texture too.
Many current Speedlites have a flash head that tilts, allowing ceilings and walls to be used as large reflectors to create more diffuse light sources and directional light. However, fractional repositioning of the camera or lack of nearby walls or ceilings limits this approach.
Flash is often used not only because a scene is dark, but also to balance shadow elements in a scene with the ambient light. Canon cameras can expose the ambient and the flash elements in the picture automatically. If the results are not as expected there are separate controls for exposure compensation and flash exposure compensation on the camera.