Even though reflection and refraction of light are important concepts in optics, they are often confused. The two concepts are unraveled here.
All the light that we see with our eyes is found in a small band in the electromagnetic spectrum. This spectrum also includes X-Rays and radio waves. Light and matter are intimately entwined. At the quantum level electrons hold atoms together, but photons hold electrons in their shell positions (add more to pop an electron out of a shell for example), and they flit between other particles carrying information.
Photons are the particle manifestation of electromagnetic waves. Reflection and refraction are the actions of waves, whether they are sound, light, or something else. The actual photon interaction with matter during reflection and refraction is very complex. Luckily for the purposes of optics the quantum interaction is irrelevant. In the context of refraction and reflection, it is important to think of light as a wave, not particles.
Light reflects when it bounces off the surface of a material. It bounces away at the same angle that it hits the material. So if it hits at an angle of 25 degrees, it will bounce in the opposite direction at 25 degrees (the total angle being 50 degrees).
There are two types of visible light reflection. Specular reflection occurs on a smooth surface where all the light hits the surface at the same angle, and reflects at the same angle. An image is reflected back. Mirrors produce excellent specular reflections.
Diffuse reflection occurs on a rough or textured surface where the light hits the material at the same angle, but since there is microscopic variations in the the surface, the light reflects in different directions. No discernible image is reflected back.
Light refracts as it passes through a material. It's direction changes, but it still passes through. Light travels at a maximum speed -- the speed of light in a vacuum, but when traveling in anything else it slows down. Different materials slow the speed of passing light at different rates. This property of matter is called the refractive index. When refracting, light doesn't change it's frequency, but since it changes it's speed, it must also change it's wavelength (it gets squished or elongated). Frequency, wavelength, and speed are all related, so if one property changes, another must as well.
A common analogy is to think of soldiers marching from dry land into a marsh, at an angle. The marsh slows down the first soldier, but since all the other soldiers across must keep in line, the whole line of soldiers ends up changing direction slightly. With light, the soldiers are photons and the whole line across is a wave.
Materials can reflect and refract light at the same time. The light comes from different directions and of different frequencies and interacts differently with the material. A good example of this are the double sided mirrors often seen in police dramas. Another example is a standing body of water.