In File Server Database approach the data is stored in the file and user have to take data directly from the file. When any change is to be made it is directly on the file application that is open .The file and data writes to these files. If 10 users are online on data then 10 are working and writing on the file.

In a client server approach data is still stored in a file but controlled by a server all the access in the hand of server. When any of application wants to make use of existing data then application request is send to server. After that server reads the request and send feedback. When any of application wants to writes something on file the request is send to server the server writes on the file. One single person reads and writes from this data files.

Oracle, Informix, Microsoft Sql Server are the best suit example of client server databases. Single user desktop just like Microsoft access.

There are lots of advantages of client server databases.

1)Single program reading and writing data the less chance of accidental changes or crashes of data.
2)Only single program play good role of security so enforcement of security is easy.
3)Client server databases use network bandwidth more efficiently then file server databases.
4)All things are handling by single computes so performance is good and quite impressive.
5)Client-servers databases use some good features that protect our data just like logging transactions and recovery from disk and network errors.

Some of these features are also available in file server approach but these need more expensive client server market. You can also learn more on dot net interview questions.