I did a series of articles over at Improve Photography testing a ton of lighting equipment. I only wanted to test the basic stuff that starters would be looking at so it was mainly reflectors, umbrellas and soft boxes from different companies.
A white umbrella is an inexpensive piece of gear anyone ever using a flash should own. It is easy to use, effective and very cheap. The umbrella is pretty self-explanatory as it works like any other umbrella and you just have to open it in front of the speedlite. The only thing to prepare for is making sure you have a flash bracket with an umbrella holder. I use a cheap one I got off amazon for $6 and it works fine.
So, why do you need an umbrella? Without something to soften the light, you get a harsh light on your subject and shadows. That can be fun to work with, but it is not very flattering in most situations.
Hopefully you can tell the umbrella does a great job of spreading a lot of light on the scene as this room was dark enough I could not see the subject through my view finder (my excuse for missing focus!), but with the umbrella and a reflector, the whole scene is lit with a nice soft light. The umbrella and white reflector produce a very nice neutral light that is bright and clean.
Be sure to check out all of our favorite lighting gear at our Recommended Gear Page.