Interesting question! At the fundamental level, it's about what light is and how it reacts with matter. Maybe you've heard that light is just electromagnetic waves - just like water or sound (which is air waves!), except instead of water or air transporting the waves, it's the electromagnetic field; you can try to picture it as electric and magnetic fields oscillating up and down. Now, remember that matter is made of atoms, which are made up of negatively charged electrons orbiting positively charged nuclei. Well, what happens to a charged particle in an electric field? It moves! So when the electric field in light hits the electrons in matter, the electrons jiggle up and down. But when a charged particle moves back and forth, it emits more electromagnetic waves! So the process is this: light hits electrons in matter, the light makes the electrons jiggle, and the electrons jiggling give off more light. The light that the electrons jiggling give off is what we call reflected light. Depending on how the atoms and electrons are arranged, the reflected light can look differently - in a metal, for example, the electrons are arranged in a way that causes the light to be reflected at the same angle at which it hit the surface; this is called specular reflection, and is basically the kind of reflection you get from a mirror. There's also diffuse reflection, which is much more common, where the light that hits a surface gets reflected in every direction; that's the kind of reflection you see off of anything that's not shiny.

I hope that clears it up a bit!

Reflection can happen for a couple reasons.Reflection off metals (like a mirror) happens because electrons in the metal happen to be able to match the frequency of the light, so it bounces off. It can also happen because of a change in refractive index. Glass and water both have different refractive indices than air, so when there's an interface between air and water or between air and glass (an interface is where two things meet), you get reflection. This is why you see reflections off glass or off water, or other materials that are normally transparent.