How does compounding interest work with a retirement fund?

I’m a bit confused here. People say that if you have $10,000 in a retirement account, the interest will compound over time, leaving a sizable nest egg from which to retire. Now, I get how compounding interest works with loans, mortgages, etc. because of the recapitalization—in that the interest gets added on to the principal every month, and then interest gets added on to that increased principal, etc. and the process repeats until you make regular payments which exceed the interest assessment on that principal.

But with an IRA or 401k, it seems that the total value is always tied to the number of shares you have and the per-share value of the stock/mutual fund you own. So it seems that you wouldn’t take advantage of compounding interest, because your gains are never recapitalized back into your “principal investment.” It would seem then that the gains would be fairly linear over time. I suppose I don’t get how just leaving $10k in an investment account with medium risk (let’s say 15%) is going to grow at more than a simple linear rate without any recapitalization.

Any help would be appreciated!