Where n is a number >= 2, describes when an application uses components on various computers in a network.
A real life example is
Everything2, the program logics of the application and the
data storage are handled by a
server. Here by making sure all the clients (who in this case use their nifty little browser apps to access the data) will use/have the same content.
Basically, n-tier apps allows for thin clients. Where servers handle data storage + business logic, thereby centralizing application logics. Making this kind of solution very: maintainable (every client does not need to be updated when application logics change), scalable, performance and extendability (very easy to integrate with other servers).