Okay, if you're still interested, let's discuss Nicotinamide Adenine Dinucleotide in its reduced form.
Put simply, Nicotinamide Adenine Dinucleotide (NAD+) is a "cofactor" in cellular metabolism. A "cofactor" is a molecule (chemical compound) necessary for an enzyme to function. It's called a "dinucleotide" because it's a group of two nucleotides (one is nicotinamide and the other is an adenine nucleobase) which are joined together by a phosphate group. You can think of it as a double railcar joined together with a link, that moves material from one station to another to allow the work at the receiving station to progress.
The simplest way to put what NAD+ is/does is that it moves electrons from Point A to Point B, so the station at Point B can use the electrons to perform a job. NAD+ "picks up" a Hydrogen molecule (one electron), becomes NADH, then essentially deposits the electron and becomes NAD+ again. The electron is now in the mitochondria (remember your teacher calling it the "power plant of the cell"?), helps generate ATP, and the product created is used to power the specific function of the cell.
Probably the best studied use for NAD+ is improved cognition. A massive study of mice showed that those with signs of cognitive impairment improved fairly dramatically with large, frequent doses of NAD. Remember, that's just mice, but brain functions are very similar in most mammals, suggesting improved cognition in humans who use NAD is likely. Many physicians use NAD infusions or injections to fight the effects of Parkinson's and Alzheimer's. A complete, double-blind, controlled study hasn't been conducted in enough humans to determine if people without any mental impairment benefit from NAD to the extent of increased mental capacity/function, but it's certainly a logical conclusion that they would. WebMD says "NADH is used for improving mental clarity, alertness, concentration, and memory; as well as for treating Alzheimer’s disease and dementia." They do go on to say that there isn't sufficient testing to prove that it works effectively, but until there are prolonged, placebo controlled, double-blind studies in large groups of humans, we won't have all the data we need.
NAD+ has been shown in clinical studies to improve liver function and repair liver damage.
Other than focus, the most common use for NAD is to combat chronic fatigue. WebMD (again) does say that NAD has shown effectiveness in fighting the symptoms of chronic fatigue, which makes sense as NAD is used by your mitochondria to increase metabolic rates in cells. Athletes worldwide have been using NAD infusions and supplements to enhance performance, though many sports governing bodies have added NAD to their "performance enhancing drug" list, prohibiting its use in many sanctioned events and leagues.
Here's the one you're all waiting to hear: Does NAD extend your lifespan? You can't really expect us to say "of course it does". Here's what had led to that claim: In 2013 a study was published in Neurobiology of Aging that had results which suggested that the deterioration of cognition was slowed significantly, if not reversed, in mice which were given increased levels of NAD. That's not to say that a 60 year old suddenly stops aging, but that the decline of the cells tested almost entirely halted. Now those mice were given a boatload of NAD, and they certainly weren't checked for other possible long-term side-effects, but the data did suggest that the expected age-related deterioration of the studied cells halted. You make of that what you will. We wouldn't claim anything other than that we read the study and it excited us too.