The terms 'action' and 'keywork' are, to some degree, interchangeable.
However, there are subtle differences between the two - as will be explained.

The keywork refers to the physical stuff....ie the keys themselves, and their component parts - the action refers to the way in which those components act.
For a more detailed description of the keywork, have a look at the Keywork page.

There are three main physical components that go to make up the action: The keys themselves; the pivots upon which they, well, pivot; and the springs, which power the keys.
Lesser physical items include the cork or felt buffers which cushion the keys.

Here's a typical group of keys...

You may have heard the term 'action' used in several ways. Players often refer to 'a fast action' or a 'low action' - repairers often talk about 'a loose or sloppy action'. The really unlucky players get to use the phrase 'a stiff action'.
So lets deal with these terms one by one - starting with 'a fast action'.

The 'feel' of an instrument relies a great deal on its action. Many components have to work together in harmony to produce a good action - the pivots must be well lubricated and tight enough to provide a smooth movement, yet not so tight as to bind.
The springs must be set at the right tension to counterbalance the weight of the keys and have sufficient power to raise the keys smartly when they are released - they should not be so strong as to excessively resist the force applied against them.
Finally the keys must be set to the optimum height, which is judged by the distance between the top of the tone hole and the surface of the pad.

But surely the less a key has to move, the better the action? Why not set the keys as low as possible?
Because there is a tradeoff. There is a 'golden point' at which the height of the action gives the best feel and speed with the best tone. Lower the keys too far and you muffle the sound - and you may even flatten the pitch of certain notes.
Raise the keys too high and the instrument responds unevenly - and again there is the risk of tuning problems.

Some horns are built in such a way as to tolerate a lower action than normal - and this, combined with a carefully balanced set of keys allows the repairer to capitalise on these inherent strengths to produce an action that is highly responsive without apparent loss of tone.
A classic example of an instrument capable of sustaining a fast action is the Conn Underslung alto saxophone.

It is possible to have a fast action when the keys are set higher, but it requires a great deal of skill to set up and a well made instrument (or you could just get lucky!).

As you will probably realise, the above explanation pretty much covers the 'low action' term too.
However, the two do not necessarily go hand-in-hand. Because of the setup that some players use (and by setup I mean the reed/mouthpiece combination, and sometimes other factors such as the pad reflectors/resonators) they can afford to lose some of the instrument's 'built-in' tone, relying on their technique and setup to replace it - though you really do need the right sort of instrument, the right mouthpiece and a good technique.

So what of the loose or floppy action?
The physical movement of the keys on their pivots creates friction. Friction=wear. The pivots are generally made of steel, the keywork of a softer metal such as brass or nickel silver - so it's the keys that wear first.
Of course, you cannot stop this process - but you can delay it by oiling the action.
Other factors that lead to a sloppy action include damage to the body (thus throwing the pillars out of line), pivots working loose (ironically enough a common problem with new instruments, where the action is tight..but not stiff) and plain old duff manufacturing.

Such an action can have a far worse effect that merely making the instrument feel uncomfortable...it can cause leaks, which lead to poor note production and intonation. It's also one of the more labour-intensive problems to fix, and therefore quite costly.

A stiff action is a terrible thing to have. As mentioned, it's not the same as a tight action. A tight action is a new action, nice and slick...quiet and positive - and a little wear will serve only to enhance the feel as the instrument is 'played in'.
By stiff I mean slow and awkward, with binding or even stuck keys. Nine times out of ten this will be down to rusted steel pivots - with perhaps the odd bent key thrown in for fun.

As for the lesser factors that contribute towards the action as a whole there is a great deal of tweaking that can be done with regard to springs and key corks.
There are four factors that affect spring action: The diameter of the spring; its length; the material its made of and the degree of offset bent into it.
As springs can be quite complex things there will be a page devoted entirely to them soon, with details of how to replace the odd broken spring.

The key corks are an important part of the feel of the action as it's they that cushion the action against the body and determine the height of the keys. Badly set key corks can lead to a clunky feel..this is known as double action. This occurs when a key cork wears or is compressed. On most instruments pressing one key down actuates another - hopefully at the same time. If you press such a key down and feel a slight clunk, take a closer look at what's happening. You'll most likely find that the key you pressed down moves a millimetre or so before it moves the key it's connected to. Try the F key - on saxes and flutes this links to the Aux.F key above it.
Clarinettists should try the middle F, this links across the middle tenon joint. Or try the low E key, which links to the low F key.

You can remove this double action by replacing the cork...but which one? Get it wrong and your new cork will prevent the pressed key from closing, or simply move the double action further up or down the instrument.
The practice of removing this double action and ensuring all the keys close as they should is known as 'regulating the action'. If your instrument exhibits double action then it is said to be 'out of regulation'.
Some instruments may have felts fitted instead of cork. In certain circumstances this gives a quieter, slicker feel to the action.