Difficulty understanding the concept

I’m used to client-side programming, and until today, I didn’t realize what difference was between server-side and client-side programming. I now understand the difference and also the difference between static and dynamic web pages. However, I’m having a lot of trouble wrapping my head around languages and server models. I’m not getting how they mix with html…or do they? And what is the point of includes/do you edit them the same way you would any other html page?

Sorry for all the questions, but I really am confused by this topic.