The principle is based on the fact that during the investigation period red blood cells in blood vessels release oxygen in active regions of the brain.

This can be detected by the computer tomograph as signals which are so sensitive that even fine fluctuations are noticed. This fluctuations indicate brain regions that just communicate with each other. Regions swinging synchronized are considered as functional networks.
Probands or patients are placed in the MRI tube with the request to do nothing and to do not focus on anything in particular.

Amongst others the device is already being widely used in Alzheimer's and schizophrenia research, to study processes of the visual cortex or to investigate tinnitus.

For more information:

Jasmeer P. Chhatwal, Aaron P. Schultz, Keith Johnson, Tammie L.S. Benzinger, Clifford Jack, Jr., Beau M. Ances, Caroline A. Sullivan, Stephen P. Salloway, John M. Ringman, Robert A. Koeppe, Daniel S. Marcus, Paul Thompson, Andrew J. Saykin, Stephen Correia, Peter R. Schofield, Christopher C. Rowe, Nick C. Fox, Adam M. Brickman, Richard Mayeux, Eric McDade, Randall Bateman, Anne M. Fagan, Allison M. Goate, Chengjie Xiong, Virginia D. Buckles, John C. Morris, Reisa A. Sperling (2013): Impaired default network functional connectivity in autosomal dominant Alzheimer disease. Neurology 81. DOI 10.1212/WNL.0b013e3182a1aafe

Colm G. Connolly, Jing Wu, Tiffany C. Ho, Fumiko Hoeft, Owen Wolkowitz, Stuart Eisendrath, Guido Frank, Robert Hendren, Jeffrey E. Max, Martin P. Paulus, Susan F. Tapert, Dipavo Banerjee, Alan N. Simmons, and Tony T. Yang (2013): Resting-State Functional Connectivity of Subgenual Anterior Cingulate Cortex in Depressed Adolescents. Biol. Psychiatry.

M. H. Lee, C. D. Smyser, J. S. Shimony (2012): Resting-State fMRI: A Review of Methods and Clinical Applications. AJNR Am. J. Neuroradiol. 10.3174/ajnr.A3263

German newspaper article:
http://www.zeit.de/