Client side programming includes any coding or computation or effects or annimation or any sort of interaction your website performs with the user via browser. But server side programming is that which performs all the task in the server only. So the user is unaware of that.
For example, PHP is used for server side programming. You design a website with HTML and use JavaScript in it to take some input from user and modify it in anyway. To be more specific, if you created a blog website and you want to specify that the user can post a max of 5000 characters. Then you do some client side programming with JavaScript to count the number of characters and any filtering or anything. But then you need to send those posts to the server. The server then performs some server side task, may be with PHP, to sanitize the input for SQL Injection and saves it into a database.
User will only know what happened in the browser but not what happened in the server. Those are background tasks.
