Interest each period is charged on what is still outstanding. At the start that balance is close to the full amount borrowed, so most of a level payment is consumed by interest and only a little comes off the balance. Because the balance is slightly smaller next period, slightly less interest is charged, and slightly more of the same payment reaches the principal. Repeat that a few hundred times and the mix inverts.

This is also why an overpayment made early is worth so much more than the same amount paid late: it removes principal that would otherwise have been charged interest for the entire remaining term.