Welcome to classic wristwatch
The history of the wristwatch is firmly tied to the military. As is often the case, it evolved to make the fighting of war more efficient, and was later adopted by the civilian poulation.
The standard watch worn by gentlemen before the early part of the twentieth century was the pocket watch. A nice substantial lump of metal, commonly attached to a waist coat button hole by a chain. It was kept in a waist coat pocket, away from the elements and safely protected. It could be drawn out to read the time, weighed in the hand and admired. The wealthier the owner, the better the quality and the more exotic the metal the watch and chain would be made from.
Soldiers who found themselves fighting in the wars of the late 19th and early 20th centuries discovered they needed access to their watches in battle. The use of the heavy field gun and timed artillery barrarges, and going 'over the top', meant time and timing was important. Gunners had to know when to start and advance the fire, and troops had to know these timings in order to advance behind the exploding shells. They found it difficult to use a pocket watch, as they were carrying heavy equipment and wearing military clothing. The result was that the watch moved from a pocket to the wrist, where it was easier to read. Initially, the pocket watch was held in a pouch attached to a wrist strap, then a heath robinson clip device emerged. A strap with a metal cross attached. The cross had hooked ends and was spring loaded, and the watch was clipped in.
Then enterprising men soldered wire lugs to the watch cases and attached straps to the lugs. Because pocket watches were so large, manufacturers soon made smaller versions of those early wristwatches, termed wristlets at the time.
During the same period, civilian men were still wearing their trusty pocket watches. Only women were starting to wear wristlets, as pieces of jewelery. They were considered effeminate and real men would never consider wearing one. A common saying by men at the time was 'I'd sooner wear a skirt than a wristlet'.
The end of the first world war changed this thinking. Soldiers returned home as heroes, and they were wearing watches on their wrists. How could that be considered unmanly? So slowly the convenience of wearing a watch on the wrist, and the changed perception of doing so, meant the wristwatch emerged as the best way to wear a watch.
Because these watches were now more exposed to the elements, some way of keeping out dust and moisture had to be developed, especially in the terrible conditions of war. Many attempts were made by different manufacturers to do so. One was Francois Borgel, who sealed the case by screwing the front and back on to a central housing. He sealed the crown by overlapping tubes. These early attempts were only partialy successfull, and the first really waterproof watch was invented by a man called Hans Wilsdorf. He invented a sealed case and a crown that could be screwed on to a taper, that completely sealed the case. He called it the Oyster, as like that sea creature, it could seal itself to be completely water tight. Hans Wilsdorf was the man behind Rolex, and the Oyster case is still a famous Rolex attribute. Note that Oyster refers to the Rolex case design, not the model of watch. The early Oyster cased Rolex watches were not perfect, as the crown had to be unscrewed daily to allow the watch to be wound. This caused the threads to wear quickly. When Rolex developed an automatic movement, which they termed 'perpetual', for their watches, the problem was solved.
Once it was firmly established, the wristwatch was refined in many ways. Automatic winding movements, more accurate designs of movement, and case and dial design all changed over the years. Specialist watches for the aviation industry, nautical use, watches specifically designed for divers, pilots, sportsmen, doctors and many other specialists were produced. Some of the very best quality and most superbly designed wristwatches were made in this period
Then came the new Quartz contolled watch, in the 1970s. It was very accurate, revolutionary and futuristic in design. It could be produced much more cheaply than a fine mechanical movement, and could keep more consistent time. It virtually destroyed the mechanical watch making industry for a while. Fortunately, people have since realised that wearing a watch is about much more than telling the time, and the mechanical wristwatch is now poplular once again. For me, the golden era of mechanical watches was from that period before the Quartz watch arrived. A period where quality and design were at their very best.
Although the Quartz movement could keep more consistent time, it also lost or gained in the same manner. If it lost a second a day, it would do that all the time. Only adjusting the time with the crown every so often would compensate.
A mechanical watch that loses or gains a little can have that  partially compensated for by leaving it stored in a certain position. When it is not being worn, storing it in various positions will affect its time keeping because gravity has a small effect on the movement. It is, therefore, possible to regulate how it keeps time to an extent, which cannot be done with a Quartz watch.
Positions a mechanical watch can be stored in are:  dial up, dial down, crown up, crown down, crown right, half way position crown up or down. Testing the various ways of storing a piece will determine which ones make it gain or lose by varying amounts. Once it is determined how the watch is keeping time, a position to store it in can be determined. Doing so will make it keep time more accurately.
Watches in space
The first man to go in to space, to orbit the earth, was Yuri Gagarin of the then Soviet Union. He flew one earth orbit in the Vostok 7 capsule. It is thought that he wore a Sturmanskie pilots wristwatch, though it is not confirmed. The watch was not specially tested or commisioned for the flight, it was standard issue to Soviet military pilots at the time.
The next man who flew in space and wore a watch of known make was Scott Carpenter of the USA. He suggested to Breitling that they make a 24 hour version of their famous Navitimer model, used by many in the aviation industry, especially pilots. They did, and Carpenter received his a few days before his flight. He flew three orbits in his Aurora 7 capsule, powered by a Mercury rocket, in May 1962, wearing his Breitling Cosmonaute.
In 1965, Alexei Leonov wore a Strela chronograph during his historic  first ever space walk. This and Gagarins Sturmanski were made by Poljot, and that manufacturers watches continued to be used in space through the sixties and seventies.
During the development of the Apollo programme, to land a man on the moon and return him safely, NASA decided to test various brands of watches for their suitability for use in space. They did not include any automatic winding watches in the tests because they were unsure they would function well in a zero gravity environment.
Before this, watches were the personal choice of astronauts and those issued to pilots for cosmonautes.
Nasa sent two technicians to buy a selection of chronographs from local jewelers. They were put through the most rigorous tests. Initially, three were ruled out. Then more tests filtered out another two. The tests included extreme heat and cold, high gravity, high levels of shock, high pressure, low pressure, vibration and accoustic noise. During the tests, one had a bent seconds hand and the other had a distorted and displaced crystal. The watch that passed and was certified by NASA for space travel was the Omega Speedmaster.
The ones NASA tested and initially purchased for use were the cal. 321 versions, and they were the ones used for many of the moon flights, although the cal. 861 was used later. These watches used elongated straps to fit around the outside of the space suit. They were subjected to the total vacuum of space, and very large extremes of temperature. The first watch on the moon was worn by the second man on the moon, Buzz Aldrin. The watch worn by Neil Armstrong was left in the Eagle lunar module, as its mission clock was malfunctioning. They couldn't risk both watches expiring out on the Moons surface, as they may have needed one on the return journey.

The Speedmaster was famously used to time a mid course correction burn during the ill fated Apollo 13 mission. There was not enough power available to power up and use the on board computer, so the Omega chronograph was used.

USA astronaut John Glenn flew a sub orbital mission in early 1962. It was the first US manned space flight. In his Freindship 7 capsule, he used a Heuer stop watch.
Although other watch brands went in to space, including Bulova and the Rolex GMT, only Omega watches were NASA certified for use in space. The digital - analogue Speedmaster X-33 was later certified by NASA, and flew in shuttle missions, amongst others.
The history of how watches went in to space is very interesting. Below is some basic information. It is well worth doing some further research as there are some entertaining tales to be discovered.