[Derekb]

As Foxy says there are basically the two types (with variations) - shoot through and reflective.

The shoot through gives a very soft light not much different to a softbox, giving nice even shadows.
The reflective umbrella has the flash head unit turned into the centre of the brolly and the light is then 'bounced' out. This gives a much harsher light with more contrast.

Just bought a full set up myself, so will be on the steep learning curve... Take a look at the Warehouse Express site, I bought the Elinchrom D-Lites and I'm very impressed with the quality and ease of use/setup.