The wikipedia article shoud be enough to explain it but, to really brief, n-tier relates to the breaking up of the project or application into seperate layers for easy design, developement and extension.
A three tier web app could be considered to be the user interface, the code (business logic) and the database.
There's really not a feasible way to demonstrate an entire n-tier architecture with code in a forum post. It generally consists of multiple projects targeting specific concerns of the application. You could do some research on the Model-View-Controller(MVC) pattern, the Model-View-ViewModel(MVVM) pattern, or the Model-View-Presenter(MVP) pattern to get yourself started.