Compounding takes place when you are able to earn interest on your interest, as well as your principle, which increases your total savings.
So basically, compounding is the process of earning interest on your interest. It is a way to grow your money faster than it normally would.
Here's an example...
Suppose Ram and Mohan both invest Rs 50,000 each in an investment avenue that offers interest rate at 10% per annum. The time duration is 10 years.
Ram chooses simple interest while Mohan chooses compound interest.
At the end of 10 years, Ram would have turned that Rs 50,000 to Rs 1 lakh. Mohan on the other hand would have turned that initial Rs 50,000 into Rs 1.3 lakhs.
In Mohan's case, the interest earned each year was re-invested along with the principal to calculate the interest for the next year.
It should be noted that the Indian stock market has gone up a huge 500x over the last 40 odd years. This is a compounded annual growth rate (CAGR) of around 15%-16%.