In photography, umbrellas look a lot like the umbrella you use to keep the rain off of your head. However, these types of umbrellas are made to work like the reflectors used on floodlights. Their main function is to provide a way of converting specular light into soft, diffused light. A good umbrella will wrap a subject in soft bounce light with specular highlights. They can be used with any light source.
Umbrellas can soften, broaden and diminish the light output any source. Umbrellas that have a white interior will soften and weaken the light more than a shiny silver lined model. A white umbrella that doesn't have a black backing can also be used as a makeshift softbox. The size of the umbrella should be determined by the size of your subject and the strength of your lighting. Some flash units are also often fitted with flash umbrellas, which are either a reflective material that bounces light back to the subject or diffusers that allow the light to diffuse through the material to reach the subject. Both of them will create a larger effective light source which will be about the size of the umbrella.
Umbrellas can range in price from about $10 to several thousand.