Keeping your style separate let's you
a) achieve a level of congruity and eases maintenance sitewide. If you have an area that should be identical across many pages, separated style lets you build it once, and use it over and over. If you want to change it, you change it in one place instead of across every page.
b) does make for lighter weight pages. Less nasty code on a page for you to have to pour through. Easier on your brain, faster for your users.
c) client computer loads your external stylesheet one time and your content just uses that.
CSS has a great deal in common with the more object oriented languages I think. You have all the cool inheritance, lots of the abstraction and...I can't remember the official name, but compartmentalization of say a Java or a C. Encourages and allows reuse.
I personally think that perhaps it's best effect on me is one I don't generally think about. It encourages me to view things in a modular sense. I'm very used to block structure in my visual design, but separation encourages me to treat my code in much the same manner. CSS lets me build a style one time and use it over and over.
Behavior - much the same thing. Your html page contains only text and lightweight pointers to your style and behavior mechanisms.
When it comes maintenance time, you notice that the little quote box that you use on 100 pages is not just right. You only have to go to your stylesheet and adjust your quote box "object" definition. Now those 100 pages are maintained, and you only needed to fix a couple lines in one file instead of doing some awful sitewide find and replace.
You notice that your function that gets called when you click a button (that you have on 25 pages) isn't doing what you want. All of those buttons call the exact same function that you cleverly defined in one external behavior file and your pages all use. You fix that one file, all 25 pages get maintained.
Separation encourages us and allows us to bring an object oriented style of discipline to something often approached monolithically.
I'm really wary though, I take everything with a grain of salt. Object orientation is not the new fancy thing it's touted as. It's just sensible in many cases, and it's been around since the dawn of computers. We just moved it from the level of instinct into our conscious minds. And even that was done in the very early 70s first. Here we are 40 years later and we are arrogant enough to regard it as some pinnacle.
It's kinda like "just in time" inventory control. It's just a fancy name for "don't buy things until you need them". An idea that probably occurred to some factory owner about 2 years after the start of the industrial revolution. He was probably beating his 8 year old orphan coal shoveler at the time.
I promised to watch my ranting, I think I might have fell short this time!