Ambient Light traditionally refers to any form of light that the photographer did not add to their image, and can include both "natural" ambient sunlight, or "artificial" ambient light such as a nearby street light, lamp, or similar. Some photographers confuse these different categories of light, and may only consider "natural" sunlight to be true ambient light.
technical explanation of ambient light
The dictionary definition of the word ambient is "relating to the immediate surroundings of something".
This is why, technically speaking, ambient light is any light source that you the photographer did not bring with you, or add or modify, before capturing a photograph.
You can modify ambient light, using a reflector, scrim, or other modifier, and it would still technically be considered ambient light, however many photographers would consider it dishonest to claim that a photograph was captured with ambient light only, and omit the fact that modifiers were used.
Between the terms "ambient" and "natural", however, there is more of a gray area that is worth mentioning. Simply put, while the term "ambient light" should always refer to any available light, be it sunlight, moonlight, or "man-made" light fixtures etc, ...some folks do consider the term "natural light" to refer only to sunlight. (Or moonlight!) This is a bit of a gray area, and to many folks "natural light" often does mean the exact same thing as "ambient light", so to avoid confusion, describing a scene's lighting in greater detail would be preferable.