N-Back helps to determine how well you can use information held in short-term memory. You are presented with a stream of letters and asked whether or not the letter you see now matches the one you just saw. For instance, if you just saw the letter H, and were now looking at the letter T, N-Back would ask you if the letter you are looking at now matches the letter H or not.
N-back tests your Working Memory. Performing the task accurately requires you to hold the identity of the last letter you saw in short-term memory, while comparing it against the current letter. The ability to hold information across short delays is important for everything from remembering a phone number to remembering why you got up off the couch.