Brace yourself for a lot of acronyms.
I have heard it said that "Techy people like you deliberately try to pull the wool over our eyes by using long technical words" I utterly refute that. Sometimes there is not a non-technical way of explaining something highly technical. The web - the way it works, the technology choices behind it etc. is a case in point. And it's changing so fast and so often that just when you think you've got your head round one lot of information it's all moved on again! Oh, and there's more, everyone you speak to will do their best to convince you that their route is the best and most advisable one!
If you want an example, get a PC user and a Mac user in the same room and ask them whose computer is better. It will not be pretty.
So, here is my attempt to explain some of the technology choices that we make and some things that affect those choices.
In 1993 when I built my first website I used a programming language called HTML. If you visited my first site (I really hope you didn't, or if you did that you don't know it was me who made it) then the pages there would give instructions to your browser to say things like "Make this bit of text bold and red" and "put this image here at the top" and your web browser would follow those instructions and present my pages to your as I had instructed it.
Things are a lot more complicated now, but the same basic principle applies. The code behind the scenes tells your browser what to do. However, the business of everything taking place by your computer processing it (known as client-side) was unsatisfactory a lot of the time because it meant I was at the mercy of how good your computer was, or what preferences you had given it. So, in order to deliver our fancy content management systems, interactive content, RSS feeds, subscriptions and e-commerce etc. we started programming with languages that did all the hard work on the server and then delivered the end result to your browser (this is known as server-side)