natural order means the transform results are in the "natural" or expected order: 0, 1, 2, 3, etc.
bit reversed order means the results do not come out in the expected order, they count in a kind of "reverse" order, with the incrementing at the MSB up to the LSB.
here is an explanation from The Mathworks:
http://www.mathworks.com/access/helpdesk/help/toolbox/dspblks/index.html?/access/helpdesk/help/toolbox/dspblks/ug/f15-8003.html memory resources can be saved with a natural => bit reversed (or bit reversed => natural) transform which is why this addressing scheme is used at all.
in most FFT algorithms, the first bin ends up as the DC component. to help people read the data, it may be DC centered so DC resides at the N/2th bin. this makes the data more natural to view since it goes from -fs/2 to DC to fs/2 (rather than DC to fs/2 to -fs/2 to DC...i think that's it i'd have to check). the MATLAB fftshift command does DC centering:
http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/fftshift.html