Here's my first draft attempt at an analogy:
If somebody could add the specific mathematics to it, if you feel it's necessary, that would be great.
You've decided to go to a fun fair, and after walking around a little, you come across a stall game that takes your fancy, you are particularly interested in it because of the prizes on offer. There is an Xbox 360 available as first prize.
All you have to do is throw a tennis-ball-like object in to a beer keg from 7 meters away. This looks fairly easy, and you're confident you'll be able to hit the target. Unfortunately it's also £10 per throw.
You know that an Xbox 360 is worth £150+, that's the same as the cost of 15 throws. You're fairly certain you can do it in less than 5 throws.
The stall holder kindly agrees to let you take a practice shot and.. bosh! Hole in one..
You step up and put your money on the counter, you're feeling confident..
Three shots and £30 later you begin to wonder if it's some kind of scam, you take shot number 4 and.. hey presto! You've done it.
You walk away with an asset worth £110 more than the £40 you paid for it. If you were to repeat this all day, you would end up with a lot of Xbox's, and after selling them, a lot more money than you played the game for.
So, taking in to account the money you spent, the money you expected to gain, and the chance of you winning it, you we're able to take advantage of a profitable activity.
Roughly a year later you find yourself at the fun fair again, you're strolling around and you come across a very similar game. This time there's an iPhone 5 begging to be yours, worth £500+ (if your crazy :P). You're looking at the prize with glee in your eyes, except "wait, what?.." Its £230 per throw!
Some quick calculations in your head tell you that, based on your previous experience of a hole in one, then a hole in 4 (2 out of 5 times), you'll make the shot every 2.5 throws. 2.5 throws will cost you £575, this is more than the first prize is worth! This time, the price to play is not attractive enough, based on your chance of winning and the prize you stand to gain.
Expected value is a measure of what you will gain in the long term, after repeating the same action a number of times.
If you are able to play poker and take advantage of the positive expected value of hands, when the odds to call are on your side, you'll be able to turn a profit in the long term.