What is a full frame camera? What is so special about it compared to other 'normal' DSLR? What are the examples of these full frame cameras?

Canon 1Ds Mk I, Mk II and Mk III
Canon 5D
Nikon D3

Full frame means the sensor is the same size as film (35mm negative). That usually means two main advantages
1. Greater light sensitivity (more sensor area that receives light) and
2. Greater compatibility with 'normal' lenses (meant for film - Canon calls EF and Nikon calls FX).

At the moment, FF cams are in the higher price bracket. That will change in time, but not so soon it appears.

from
tigadee

other info http://en.wikipedia.org/wiki/Full-frame_digital_SLR