I started using a Hasselblad 500c/m last year. Almost everything I'm doing with it is portraiture. I have the standard 80mm lens, an older model 150mm lens, a waist level finder, metered prism, and a few A12 film backs (gets 12 6x6cm shots on a roll of 120).
There are different models, but the popular models are single lens reflex cameras, have a box-like body with the lens up front, a viewfinder on top, and a film holder on the back. There are a wide range of lenses, viewfinders, and film backs available.
Hasselblads used to always be 6x6cm cameras (although you can get backs that allow 6x4.5). The company could go on at great lengths why this was the perfect format. Recently they have introduced a 6cm x 4.5cm body that is being marketed mostly for digital backs, and suddenly all their 6x6 malarky has gone out the window.
There are lot's of Hassy websites out there. Just do a search on the model(s) you are interested in. Here's a great site for almost all medium format cameras to get you started.
http://medfmt.8k.com/