Server Side This is code/routines executed only on the server. Code can be written in scripts as well (vbscript usually), but in the case of ASP.Net this is the compiled lanuages like C# / VB.Net. Used for processing content and returning data.
You call up a webpage and a message box appears saying Welcome to "my site". This is client side. It did not require any request from the server to have that message box appear. That code was run on your computer/browser. But the page you requested displays a list of movies playing in your town. That list was populated/retrieved through a call to the Database (located at the City movie repository...or whatever) i.e. the server to retrieve that data for your town.
Letscode: that isn't quite right. The "HTML" view in the VS.NET IDE isn't really HTML. It's ASP.NET code, or "aspx" code. Here you'll find the declaratives used by ASP.NET, along with the code-behind, to generate HTML. In other words, this isn't client-side code. What you see is still processed by the server.