You might be able to try a paint analogy, like the one commonly used to explain the Diffie-Helman key exchange:
Imagine a game of roulette where the number on the board was determined by a shade of paint, and every shade of paint had its own number. The number of shades of paints is very large, because you can always change it by mixing just a little more of some other paint in.
The house starts off by picking their own color of paint, but they want to keep it secret. So the house mixes their secret color with a special paint and shows you the mix. You can't tell what their secret color is from this mix, but this will come into play later.
Next, you come up with your own color of paint, and give it to the house.
Then, the house mixes together their secret paint (that you don't know), your paint you gave them, and one more color color that changes every spin. (This last color is something that you know, so imagine they just pick red, orange, yellow, green, blue, etc. every time but they have an infinite amount of options). The color they get once they mix everything together is what they use to pick the number in roulette! Now, why couldn't they just pick a number by themselves without all that stuff in the middle?
Since you gave them your color before they mixed the paint together, you changed the outcome in a way they couldn't expect.
This means that the house does not have any control over the shade of paint, only the way they use the paint to get a roulette number
Now, you've finished betting for the night. The house shows you their secret color! To make sure that they were doing what they said they were, you take their secret color and mix it with the special paint just like they did in the beginning, and you see that it made the same mix as the one they showed you at the beginning. This is important!
This means that the house was doing just what they said they were doing
If you wanted to, you could mix the colors yourself to see what the results are yourself, i.e. now that you have the house's secret color, you mix it with your color and the color that changes every spin (remember, you know the color that changes for every spin, let's just say it's red for the first spin). You get a mix of colors and find out that the mix corresponds to the number from the first spin on the roulette wheel. Yay! The house isn't cheating you!
The house's secret paint is the server seed.
Your paint is the client seed.
The paint that changes every round, is the nonce (A nonce is just a number that usually starts at 0 or 1 and goes up by one for every bet you make).
The special paint is a cryptographic hash function, which is a special function that takes in any data and gives you a different piece of random-looking data. The important part about the hash function is that it's one-way: If you only have the result, you can't use it to get what was originally put in the function.
Provable fairness isn't one particular method or set of actions, it's more of a general set of rules:
The user must somehow influence the result - This is provided by the use of a client seed
The game must operate in a way that shows the result could not have been altered in the favor of the house, or in any other way - This is provided by the hash of the server seed
Hope this helps, it could probably be more friendly but that's what I came up with on the spot.