The Coriolis force is a theoretical force used to account for the odd behaviour of objects which move far enough in rotating frames of reference. It is related to centrifugal force, and is a similarly convenient fiction.
The Coriolis effect - which the Coriolis force is often used to account for - is named after Gustave Gaspard Coriolis (1792-1843), the French mathematician and physicist who first described it in 1835 in a paper entitled On the Equations of Relative Motion of a System of Bodies.
Newton's Laws and Frames of Reference
Newton's Laws apply, in full and unmodified, in an inertial frame of reference. This means that if the place where you are doing your experiments is either standing still, or is in uniform motion, ie not accelerating or decelerating in a straight line, all your experiments will agree with Newton's Laws. However, if your 'lab' is undergoing any kind of acceleration, either in a straight line or in a curve ie, it's either rotating, orbiting a point or simply moving in curve, you will notice some strange effects.
An example of an inertial frame of reference is the whole universe (as far as we know...). Unless you have some seriously accurate measuring equipment, another example of an inertial frame of reference is a room in your house. Even though your front room is on the surface of the Earth, and the earth is rotating, practically any experiment you do will suggest your frame of reference is inertial.
However, if you take the whole planet as your lab, things are very different. The Earth is most definitely a rotating frame of reference, and some of the effects of that are very odd indeed.
How to Tell if You're in a Rotating Frame of Reference
As stated above, in ordinary life, just walking around, we usually think we're in an inertial frame of reference. Things stay still until you push them, and when they move, they generally move in a straight line unless acted on by some other force. This is the first of Newton's Laws, and without it snooker would be impossible, or at the very least a lot more difficult. All these things reliably apply to most stuff at the scale of a single human.
However, since we're on the surface of a spinning sphere, we're actually in a rotating frame of reference all along. To us on Earth this is actually fairly obvious: one glance up into the sky won't tell you, but another six hours later should give you a fairly hefty clue. The sun and stars demonstrate to us that our planet is rotating, and eventually Copernicus took the hint by looking at the paths that the other planets seem to take in the sky. But if we (like the people of the planet Krikkit in Douglas Adams' Life, the Universe and Everything) lived on a planet inside an opaque dust cloud, with no outside cues to help us realise our frame of reference was in fact rotating, would we be able to do an experiment to tell?
Well, the answer is yes - but in essence, a very simple experiment. Stand at the equator1 and fire a missile. Aim it to land exactly one thousand miles away. If you fire it due east or due west, you will note that it lands one thousand miles away in a straight line in the direction you aimed it. So far, exactly what you'd expect.
Now fire another identical missile one thousand miles due north. You will now note with some surprise that it didn't land a thousand miles away, and despite your perfect aim and the complete absence of any wind, it didn't land due north of your position either. Instead, it appears to have veered off to the west. Why?
A simple way of interpreting this occurrence is that some force diverted your missile. To you, standing on the ground, some force is surely required to explain the fact that the missile didn't travel in a straight line as predicted by Newton's first law. But what generated this force? To an outside observer, however, in an inertial frame of reference, the truth is clear. Your missile travelled in a perfectly straight line - but while it was up in the air the ground moved beneath it, so that it landed on a different line of longitude than the one it took off from.
Of course, since you are moving along with the ground, you cannot directly perceive this. You can however, infer it from the behaviour of other objects.
The Dead Giveaway
So, does Coriolis force actually exist? No. Real forces, like gravity, have a source, such as mass. Coriolis force is, like centrifugal force, a convenient fiction designed to account for the discrepancy between the normally reliable Newton's first law, and actual experience in rotating frames of reference. The dead giveaway here is that Coriolis force is a 'force' which applies to things you throw to the north, but not things you throw to the east, and you can't have laws which work in one direction, but not another: this is akin to having, say, gravity affecting things in the northern hemisphere, but not in the southern hemisphere - unthinkable.
If it Doesn't Exist, Why Does it Have a Name?
Coriolis force is as the title says, a convenient fiction. Using equations which include Coriolis force can simplify many calculations, including weather prediction and trajectories of ICBMs (Inter-continental Ballistic Missiles).
To experience Coriolis force for yourself, try throwing a tennis ball to a friend while you both ride on a roundabout. For maximum effect, don't stand opposite one another.
So That'll Explain the Bathwater Swirling, Then?
It is often said that it is possible to tell which hemisphere you're in by looking at the direction in which bathwater swirls down a plughole. This is put down to the Coriolis effect, but on the day to day, normal human scale of things, the Coriolis effect is tiny. This is one of the reasons why nobody noticed it until 1835. In fact, other factors such as how the bath was filled, who got out of it and how long ago, and the precise shape of the bath will have a much greater effect on the direction in which the water swirls.
Will it Ever be a Problem?
For most people, the Coriolis effect is something they will never notice. However, it is reasonable, if a little optimistic, to assume that at least one person who reads this Entry will spend some time in a spacecraft which simulates gravity by spinning. Unless that spacecraft is enormous, Coriolis effects will be immediately obvious to anyone who tries to spin around in a swivel-chair: they'll fall over. For this reason, there may be pressure to build ever larger habitats, until the 'threshold of obviousness' for Coriolis effects is passed.