How does the n-back test work?
Letters appear one at a time, each for 0.5 seconds, one every 2.5 seconds. Press Match when the letter on screen is the same as the one N letters before it. In 2-back, for example, the sequence K, R, K has a match on the second K. You choose N: 1, 2, 3. A tick or a cross confirms each press, so you learn the rule as you go.
How is your result calculated?
20 letters are scored, and exactly 6 of them are matches. Every scored letter is a decision: pressing for a match is a hit, letting a non-match pass is a correct rejection. Your result is the share of decisions you got right. Missed matches and false alarms (pressing when it wasn't a match) are shown separately, because they are different mistakes.
What does the n-back test measure?
Working memory: holding a few items in mind and updating them as new ones arrive. Every letter forces you to drop the oldest one you were holding and take in the new one, so the task gets much harder with each step of N. It was introduced by Wayne Kirchner in 1958 and is now one of the most used tasks in memory research and brain imaging.
Does n-back training make you smarter?
Probably not. A 2008 study suggested that practising a dual n-back task raised scores on reasoning tests, which made n-back training popular. Later work did not hold that up: a 2016 review of 87 publications by Monica Melby-Lervåg, Thomas Redick and Charles Hulme found that working memory training improves the trained tasks and similar ones, but not intelligence or other distant skills. Practise it because it is a good challenge, not as brain training.
For other working memory tests, try the Digit Span Test or the Chimp Test.