Compounding means your returns start earning returns. The reason it feels underwhelming is that it does almost nothing for years and then does almost everything at the end — the growth is exponential, so the largest absolute gains arrive last. Someone who invests for 40 years doesn't get twice the outcome of someone who invests for 20; they can get several times as much, because the final years operate on a much larger base.
This has one dominant practical implication: time in the market beats timing the market, and starting early beats starting big. A person who invests a modest amount from age 25 to 35 and then stops can end up ahead of someone who invests more from 35 to 65, purely because the early money had more time to compound. It also means the biggest financial mistake is usually not a bad investment — it's a late start, or interrupting the compounding by selling in a panic.