In Bridge, What Is "Playing the Card You Are Known to Hold?"
Great question!

The basic idea is that by playing the card you are known to hold, you do not give declarer any extra information and might mislead declarer about the length of your holding in that suit (the falsecarding bit).

(btw, your example about west leading Q and you playing K from Kx not to disclose your A is not completely right. If East has the A, he will play it. And West would likely not lead the Q from AQ {unless an NT contract, of course}. So the location of the A will probably be known anyway...)

Anyway, here is an example with respect to defense.

      AQJx
      xx
      xxx
      AKJT
Kxx          xxx
xxxx         xxx
xxx          xxx
xxx          Qxxx 
      xxx
      AKQx
      AKQJ
      xx


Playing Matchpoints (note: overtricks matter here) South the declarer, finds himself in 6NT.

You are West and you lead a heart.

Declarer wins and plays a spade to the J which wins.
Now declarer comes back to hand with a diamond and leads another spade.

At this point, you must play the card you are "known" to hold: the K.

The K is going to drop on the A anyway, so it is not as if you are wasting that card.

Consider:

Declarer has 12 tricks and would be trying for the 13th (remember, this is matchpoints).

To try for the thirteenth, declarer has two major options: spades 3-3 or club finesse. (we are ignoring any squeezes to get the point across, and IMO those chances are inferior anyway)

If you play low instead of K, declarer will know that you started with either Kxx or Kxxx.

In either case, declarer can cash the third spade to test for spade 3-3. If spades are 4-2, he can safely take the club finesse into partner's hand, who has no spades to cash.

So if you play low, declarer can combine his chances of spades 3-3 with the club finesse without endangering the contract and in the current layout, he will make 13 tricks.

Now imagine you played the card you are known to hold, the K.

Now declarer will likely place you Kx, (but a smart declarer will not completely eliminate Kxx, or Kxxx, of course).

Now if declarer tests for spades 3-3 and you indeed turn up with Kx, declarer is in danger of losing his contract if the club finesse (for the 13th trick) loses, as partner can cash a spade when he gets in.

So in order to not endanger the contract and having some chances of making the 13th trick, declarer might choose to give up on spades and take the club finesse.

If that happens, you hold declarer to 12 tricks, while at the other tables where the defender in your position played low, declarer makes an easy 13.

So by playing the K, you have nothing to lose but a lot to gain.

Of course, at the table you might not have time (or even need to) think about all this. The idea of not giving declarer any extra information is usually sound and when you have no clue about a hand (or need to play in tempo), it pays to follow general principles.