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Would you rather receive $100 now, or would you rather wait for ten years and then receive $100?
You'd probably want it now. Not only does money get less valuable over time, but you could invest that money and earn even more money over the next ten years.
Because you (and everyone else on the planet) realizes that it is better to receive money now, we have to compensate others when we borrow it.
This compensation is usually expressed as a percentage of the money borrowed.
Let's say that you want to borrow $50, and I agree to make a loan at 10% for a year. We can calculate how much you'll owe next year by multiplying $100 by 110%.
(The 110% has two components 100 of that is to return the principle, and the 10% represents the interest.)
That's great, but what if you want to borrow it for two years at 10%? We'd take the cost of the loan for the first year, and multiply it by another 110%, so $50 * 110% * 110%.
We can make it look a bit cleaner by writing it with exponents, instead of repeating the percentage twice. This leads us to $50 * 1.10^2.
Of course this works backwards too. If we knew that $60.50 would be due in two years, we can divide it by 1.10^2, to get our original $50.