External DAC -general questions

I've used digital to analog converters off and on for many years mostly in attempts to make resulting sound more "analog like". The only application that I was able to tell a difference, though, was when I installed one between an old Sony jukebox and a Sphinx integrated amp. In other words, I think I really added DAC's because it just seemed like it should improve the signal.

My questions may be based on unfounded assumptions but here's where I'm confused; I assume that in all of audio, for there to be amplified sound, some form of conversion to analog is necessary and would be built in to the equipment. My recent amps and preamps boast of good built in DAC's, tube DAC's at that, and I still have external converters between them and various sources. So here's the question; if an analog converted signal is being delivered to an internal circuit designed to convert from digital to analog already, how does that work. I know it does and maybe I don't need to understand it to use it, but I would like to have some understanding of it.