I'm often asked why a pendulum clock just stops for no apparent reason or why it won't run for a full 8 days anymore. To answer this you need to understand how a mechanical clock works and this page attempts to explain that in the simplest of terms, without jargon. There is a separate page on some of the common causes of why they stop working but I urge you to read the following before you visit that page.
First, you need a power source. I don't mean a battery (though the vast majority of modern clocks are indeed powered by a battery, but that's another story). The power in a mechanical clock originates from one of two possible sources. It might come from a weight, most commonly found in Longcase clocks, Vienna regulators and Dutch Zandaam clocks to name just three. The weights might be lead, iron or brass and weigh anything from a kilogram to five kilograms or more. However, most smaller clocks are powered by a heavy spring, called the mainspring. It's usually encased inside a brass barrel so you might not be able to see the spring itself. American clocks rarely use a barrel so if you can see the mainspring in your clock, it could well have an American movement.
The mainspring is made from a strip of carbon steel to enable it to be hardened so it can be set into a large coil and hold its shape. When wound up tight the natural tendency of the mainspring is to unwind back into that set position again and if it were uncontrolled it would lash out causing untold damage as it does so. Constrained by the barrel, as the mainspring uncoils, it also turns the barrel. At this stage it is so powerful that you could not prevent the barrel from turning no matter how strong your grip (but please don't attempt to prove me wrong - it will hurt!).
The brass barrel has teeth round the edge (known as the barrel wheel) which interlock with the teeth (called leaves) of a tiny adjoining gear (called a pinion), which is made of steel. The pinion is part of a steel shaft or rod (called the arbor) and somewhere along its length is a second brass wheel (called the intermediate wheel). The teeth of the intermediate wheel engage with the leaves on another pinion and turn a third wheel (called the centre wheel) on another arbor that runs through the middle of the clock and carries the minute hand on a square at the front end. It also turns the hour hand via a pair of brass wheels (known as the motion work) concealed under the dial. That centre wheel pinion also engages with the fourth wheel which is geared to the final wheel known as the escape wheel.
So the considerable power of the mainspring is reduced by a train of gears until the level of power reaching the escape wheel is more manageable. In fact, you could stop the escape wheel turning very easily with just a feather - remember this, because it will explain why sometimes it does not turn. By the way, the teeth of the escape wheel (or 'scape wheel as it was called years ago) have a very different profile from all the other wheels; it's spikey and the tips are quite pointed, so you should be able to locate it easily if you look towards the top of the movement. (In a carriage clock its teeth are cut sideways into it - and it's known as a contrate wheel. But of course a carriage clock is not a pendulum clock so I digress).
If the escape wheel was allowed to turn with no control, it would spin very quickly for ten or fifteen minutes as the mainspring slowly turns the barrel wheel, forcing it round until eventually the mainspring runs out of power. It would also damage the delicate pivots at each end of the arbors because they are not designed for that and would overheat. But the escape wheel is not allowed to spin - instead, it is controlled by the swinging action of the pendulum through the escapement, the pallets on which often resemble the two curved points of an anchor. As the pendulum falls one way, one of the pallets locks one tooth of the escape wheel to stop it turning, and then as it swings the other way and release that tooth, the other side locks a different tooth. The escape wheel therefore turns in little jumps, allowing the other wheels (and thus the hands) to turn also. And the ticking you hear is the teeth of the escape wheel slamming against the pallets as the wheel tries to spin and the pallets alternately lock it.
Now an important point to emphasise here is that as the tips of the teeth of the escape wheel eventually slip past the pallets of the escapement, gently pushing them out of the way, the action provides a little kick (or impulse) to the pendulum and this impulse is vital to ensure that the pendulum keeps swinging. It's only the slightest of kicks but it's enough to ensure the pendulum does not stop. Over the years several different types of escapement have been devised to create that impulse, some complex but efficient (Brocot, Graham, Breguet) and others simple and cheap (pin pallet, cylinder, bent strip) to mass-produce. You can watch several in action on a clever German website (in English) called CLOCKWATCH for a better understanding.