Hi, Mitch, and happy new year to you, too!
In short, the analog audio signal that represents your music or movie soundtrack is very low power and is being passed through a circuit board (or more than one) inside of the electronics. In order to be able to hear that signal from your speakers, it has to be amplified. Your question, I believe, is all about - where should I amplify it?
Receivers are loved by many and hated by some - I happen to love them. They combine multiple functions into one box: such as a pre-amp (which helps you select between sources and do some modifications to the original audio), amp, tuner...and these days, audio media streamers and other network functions.
To get everything into one box at an affordable price, the companies have to limit what all they shove in there. They often do it pretty intelligently, though, and many receivers are going to have plenty of power amplification capability for most people. I've tried a number of them in the $400-$500 range, and most do an excellent job in my set up. Let me say that again - in my set up. How much power you need depends on how loud you want to listen, which speakers you have, and your room.
My recommendation is to pick out your speakers first, then pick out the electronics that best support them. For most speakers, a receiver is just fine - and it's worth getting a receiver first and finding out for yourself if you think it's lacking. If it is lacking, then you can move on to another receiver, start looking at adding external power amplification for that receiver, or go with separate components and skip a receiver all together.
As for why people suggest an external amplifier be used for only some of the channels is that the receiver still has amps in it - they just might not be enough to cleanly amplify all of the channels. Every receiver that I've seen has a single power supply that feeds multiple amplifier sections. So, if five channels require 100 Watts each during a certain movie explosions, that's 500 W that the receiver has to handle in the amps alone. Maybe it can't do that much without clipping, but maybe it can do 400 W no problem - in that case, amplifying the front two speakers with an external amp would lighten the load on the receiver enough that it wouldn't clip when playing through the other speakers. Yeah, I completely made all of those numbers up, but it was just an example.
Anyway, amplifying only some of the speakers with external amps reduces the requirements when shopping for those amps (or amp), and it lets you use the amps inside of the receiver that you already paid for.
