Our internal 'biological clock' doesn't necessarily speed up, but the way our brain processes and stores memories changes, impacting our retrospective view of time.
While our actual biological processes, like heart rate, don't speed up dramatically to explain this feeling, the way our brain packages memories does change. When we look back at a period, our brain essentially counts the number of 'events' or distinct memories it has. If a period was full of unique, memorable moments, it feels long. If it was largely repetitive and predictable, it feels short. This is why a summer vacation might feel longer than a month of typical work days, even if they're the same length in actual time. So, it's less about time truly accelerating and more about our brain's filing system. As we accumulate more years, each new year has fewer truly unique 'files' compared to the vast library of memories we already possess. This makes recent periods seem to compress, giving the illusion of speed.