The (dual) N-Back brain exercise is supposently capable of training your Working Memory (short term memory)
And related to that -> your fluid Intelligence (Gf).
(backed up by several scientific studies)

Its basically a revolving memory game, where you have to remember if an item/letter etc, appeared "n" steps in the past.



Its still under scientific discussion, but nowhere near of beeing a hoax that is easy to disprove.
There where several studies proving this approach, (also studies not
prooving a significan effect)


The Idea is, that regular (and demanding) training will increase the efficiency of your Short Term / Working Memory and attention,
thus pushing other capabilities (such as IQ, some say by up to 10 points)
The training effect will kick in after about 20 days of training, and persists for months after.

Its a really interesting concept.

Here some useful links to versions of the game

http://www.brainboffin.com/ (Online N-Back)
http://brainworkshop.sourceforge.net/ (Offline APP, quite good)
http://cognitivefun.net/test/4 (Online) Picture single n-back, more relaxing..

some links

http://www.gwern.net/DNB%20FAQ (good FAQ page with a selection of opinions and references)
http://www.nytimes.com/2012/04/22/magazine/can-you-make-yourself-smarter.html?pagewanted=all

Original study

http://www.pnas.org/content/early/2008/04/25/0801268105.abstract
(google some to find the full paper)

BTW: dont wonder if you are dreaming much more intensely after starting the training.
Its a known side effect and (assumingly) shows that your brain "rewires"