One form of 'game' can be played like this: two players each decide on whether to 'co-operate' or to 'defect'. What they decided to do is then revealed to one another. Your score is calculated based on what you both did.
If you defect but they co-operate, you score A points.
If you both co-operate you score B points
If you both defect you score C points
If you co-operate but they defect, you score D points
A, B, C, D can take different values (agreed upon at the start of the game), and the game you are playing depends on which values you choose. In the prisoner's Dilemma, A > B > C > D. This means maximum points for defecting on them when they co-operate, and minimum when you co-operate with them but they defect.
The game standing alone is interesting if there are some stakes involved (perhaps chocolates...) but an iterated game, in which you play rounds repeatedly for a set (or unknown, random) number of times, can be fascinating.
A simple example set of values for A, B, C, D is 3, 2, 1, 0 respectively.
The important and somewhat subtle fact that I have missed out so far, is that the aim is to get AS MANY POINTS AS YOU CAN. The points (or chocolates, or money, or whatever you play for) are supplied by a 'bank', which is not a player in the game but an external 'source'.
The confusion arises when people realise that they can gain more points at the expense of the other player, and this can blur your objectives, but the game is nonetheless still effectively the same.
The 'dilemma' (as I see it) is effectively this:
If they co-operate, you want to defect - this gives you the most points (3 as opposed to 2)
If they defect, you want to defect - this gives you the most points (1 as opposed to 0)
So at any given time, to get the most points in that round you must defect. But if you both think like this, you will both always defect, and both end up with small scores - the very opposite of your aim.
There is an enormous amount of theory on this, but the conclusion seems to be this:
The Best Tactic, in general, is to do whatever your opponent did on the previous round (and co-operate in the first round).
Applications to life
This somewhat artificial 'game' actually models many situations in life very well. For example, in a game of chess in which you have no fixed time limit and are simply playing for fun, to take a very long time over a move could be regarded as a 'defection': you get the benefit of coming up with a good move, and they get the downside of not being able to plan very well and having to just sit there for a long time. This is then iterated in their move, and if you both defect then the game can become very slow.
A newspaper stand run on 'trust': you take a newspaper and put money in the box. Defection would be to break this rule and take a newspaper without paying: you get the benefit of a newspaper for free at the cost of the people who do pay, and the publisher. This also has the property common to many n-player prisoner's dilemma-style games, in that it is tempting to think that what you do is insignificant in the long term and hence doesn't matter, BUT if everyone does as you do then the whole system will collapse - someone will have to be employed to sell the newspapers (in itself no bad thing, I suppose...) but the price will then go up for everyone.
So, watch out for the Prisoner's Dilemma in your life!
Co-operate all the time! I do!
(unless, of course, you didn't co-operate with me on the previous go, in which case...)