That self-winding perpetual-movement monstrosity strapped to your forearm is accurate across a hemisphere's worth of time zones. But no matter how extravagantly handcrafted or precisely engineered your Rolex is, it'll never be as accurate as a cheap digital gas station watch. Here's why.
The earliest known pocket watch was devised by German locksmith Peter Henlein around 1505. These small, globe-shaped mechanical brass clocks, known as "taschenuhr", were worn as accessories and trinkets by the upper class, much as chihuahuas are employed today.
Besides acting as Plague-era bling, these wearable clocks marked the first use of spiral mainsprings, metal torsion ribbons that store the potential energy that drives a timepiece. The energy stores in a mainspring keep a watch ticking, but they're not limitless. Eventually, they get used up countering oscillation-impeding inertia and friction. And therein lies the problem.
See, mechanical clocks rely on an oscillator -- the watch's inner movement, or a grandfather clock's pendulum, say -- to control the system's frequency, which is how the clock maintains accurate time. But friction robs this oscillator of a tiny bit of energy on every stroke. Minute by minute, that adds up; as the oscillations slow, the timepiece's can lose a few seconds of accuracy a day. A mainspring's purpose is to counterbalance that effect, continually adding stored energy to the system to keep things on track. Winding a clock, either with the watch crown or a key, adds to the mainspring's potential energy. And you need to do it every 40 hours or so to stay current.
In addition, the mechanical watch's reliance on minute, delicate, fail-prone parts that are easily affected by temperature fluctuations and magnetism demands regular and often costly readjustments, making analogue watches more expensive and less accurate than their digital successors.
Then there's electronic movement, or crystal oscillation, which leverages a vibrating hunk of piezoelectric quartz to generate an electrical signal with a specific frequency, rather than rely on a series of gears and pendulums. Piezoelectric materials create electrical currents when stressed -- in this case, the material is expanded and contracted. Conversely, the same piezoelectric material will vibrate when exposed to an outside current. The crystal's size and shape determine the frequency it produces -- known as the resonant frequency -- typically in the kilohertz to hundred megahertz range. Early devices relied on naturally occurring quartz; however, the use of synthetic quartz is nearly universal these days.
High-stability frequency crystal oscillators -- those suitable for clocks -- were developed in 1928 by Warren Marrison of Bell Telephone Laboratories and have since become the most widely-used means of telling time in the world. Losing just one lost second every 30 years, quartz movement is orders of magnitude more accurate than mechanical designs. As such, more than two billion quartz oscillators are manufactured annually for use in personal timepieces, electronic circuits, and radio transceivers.
While crystal oscillators are susceptible to temperature, humidity, pressure and vibration fluctuations, even inexpensive watches are designed to minimise these environmental detractors. The oscillator is shaped like a tuning fork and designed to vibrate at exactly 32,768Hz (that's 2^15 cycles per second, from which a steady, second-counting 1Hz signal is derived). In addition, many watches feature inhibition compensation. That is, they're intentionally built to run fast, and programmed to a set number of crystal oscillation cycles at a regular interval. This allows the manufacturer to measure and store the timing information in non-volatile memory on the chip, rather than expend the cost of cutting the crystal precisely.
So just as mechanical clocks overtook the sun dials and water clocks before them, they too have been eclipsed by a more accurate method of counting seconds. And who knows? Digital watches giving way to something even more precise can only be a matter of time. [Wikipedia 1, 2 - How Stuff Works - NIST]