Traditional rendering solutions do not do account for secondary light bounces (called indirect light). Even with strategically placed fill lights you still have areas where none of the direct light hits.
Ambient light tries to solve this problem by shining by a constant amount in all directions. In practice this means that light position or surface normal has no meaning, one just adds some of the shaders color multiplied by ambient light color to the shading result.
Ambient light has a tendency to look artificial when overused. But the opposite problem is that surfaces look like they are on outer space. Ambient light also makes the difference between dark materials and light materials more apparent.
Image 1: Image without ambient light (left) looks like it was shot in space. Image with ambient (right) looks more natural, although possibly a bit flat if overused.
The real problem is that ambient light does not really exist. Even if youd argue that its useful model, it certainly is not uniform. Its just a quick fix. Therefore all kinds of tricks, like ambient occlusion, have been proposed to enhance the quality of ambient light.