That's a good question to ponder! First, if you imagine light from a lamp bouncing off the surface of a mirror, the mirror would look like a "light" - in fact, you'll see an image of the lamp in the mirror, as if you're looking at the lamp itself. The reason is that the mirror's surface is smooth microscopically, and all light hitting it bounces off at the same angle that it hit the mirror. Therefore, when you look at the lamp "in the mirror", you're looking at the light rays that came from the light and bounced off the mirror into your eyes. This phenomenon is termed "specular reflection" (refer to figure below).
When light from a lamp reflects off an object like a cereal box, the cereal box does not look like a light because unlike a mirror, its surface is rough on a microscopic scale. So light that hits the box does not bounce off at the same angle from which it came - and this is called "diffuse reflection" (refer to figure below). Thus, what we see when we are looking at a point on the cereal box is a jumble of light rays which could have originated from anywhere, but happened to bounce off that point and enter our eyes. The fact that you could even see the cereal box implies that light must have reflected off it, since it does not produce its own light.
Furthermore, the cereal box does not have to be of the same color with the light from the lamp because the color pigments on the cereal box absorb certain colors of light, only reflecting the remaining colors of light from the lamp. In fact, this selective absorption of colors is responsible for most of the variety of colors we see reflected off objects around us.
Hope this helps!
Image source: Specular and Diffuse Reflection http://www.colgworld.com/figs/specular-and-diffuse-reflection.png
(published on 05/24/2011)