The chronograph is for wannabe Paul Newman race car drivers who prefer messy dials yet actually drive a Prius. It's a stopwatch function built on top the time-telling watch, allowing you to time things like how fast you can walk from the couch to the fridge to get a beer, if your dog can do it faster, and how fast you can drive your Prius around your cul-de-sac.
Some of the most desired vintage watches are chronographs: the Rolex Daytona, Omega Speedmaster, or “the first automatic chronograph,” Zenith’s El Primero (which translates to "the first, but no one cares because we're fucking Zenith" in Spanish), which means that you too will be elevated to legendary status with your chronograph purchase(ideally a limited edition Speedmaster!).
A typical chronograph dial (such as the El Primero, below) is a distracting mess, the large sweeping seconds hand in the middle of the dial acts as the stopwatch. One subdial (at 3 o’clock on this El Primero) will act as the stopwatch’s minute hand, letting you keep track of how many minutes have elapsed since you started the timer. Another subdial (at 6 o’clock, here), acts as the stopwatch’s hour hand, letting you keep time for hours. You might ask "what the hell is someone timing for more than an hour? And then I'd slap you in the face for asking an exceedingly relevant question for which there is no answer.
Finally, a third subdial acts as the watch’s usual seconds hand. Sometimes, a tachymeter is added to the periphery of the chronograph’s dial. This indicator allows the user to quickly see units per hour (e.g. kilometers, miles), instead of having to do a calculation, because you probably barely got through college calculus.
The term “chronograph” comes from the Greek for “time writing,” and this is how early chronographs worked, as a small pen would attach to an index and mark how much time had elapsed. The first modern chronograph was invented in 1816, but was only developed for use alongside astronomical equipment. Then, Paul Newman came along and used it for much more practical things, like racing cars.
In the early 1900s, the Breitlings added pushers to the chronograph at 2 o’clock (stop) and 4 o’clock (reset), adding additional functionality to what, by then, had already become an extremely popular complication. This further cemented Breitling’s reputation as the brand for aviators, and it soon leveraged its innovations by creating the Navitimer, the quintessential pilot’s watch that isn't even a pilot's watch because it's impossible to read. And that's the last time Breitling did anything relevant.
Since then, chronographs have become a favorite among watch enthusiasts, often taking their place alongside historical moments or figures. Astronauts wore their Omega Speedmasters to the moon; Jack Swigert famously used his to time a 14-second fuel burn aboard Apollo 13, the exact time needed to ensure the spacecraft was perfectly aligned for re-entry to Earth’s atmosphere. Heuer had its Carreras and Monacos (the later made famous by Steve McQueen). Paul Newman famously sported his Rolex Daytona (a certain exotic dial variation now bearing his name). Wear your chrono enough and it too may become synonymous with your name, John.
A flyback chronograph allows its user to reset the stopwatch function’s seconds hand of the watch without first stopping it. This not only allows the user to measure events in rapid succession, but also allows for the measuring of intervals. For example, laps in a race can be timed with a simple press of the flyback pusher, while the aggregate time of the race is still being kept as well. Or you could use a digital stopwatch like a normal person, although I do dream of being at my kid's track meet, walking up to the official timer with his digital stopwatch, flicking my wrist up to display my Daytona, and saying, "back off bro, I got this, down to the 1/8 second." And then my kid would say "that's my dad! he waited on an AD waitlist for 16 months just to time this race!" Watches, creating memories.
The split-seconds chronograph is an even more complex and useless chronograph that has two central sweeping hands, allowing for the timing of two intervals that start at the same instant. This is referred to as rattrapante in French by watch bloggers who took more than one semester of French in college (or have visited the French side of Switzerland more than 3x), and is widely considered the most complicated of the chronograph complications. Like so many needless complications, Patek Phillipe brought the first split seconds chronograph in a wristwatch to market, in 1923.
Today the main function of the split second is to take that swords-crossed photo for Instagram.com. Oh we crossing swords bro? I know my Panerai screams BDE but my sword is actually quite small.