I suppose this is homework...
Anyway, servier side scripting is processed at the server itself; meaning all the code would be executed at the server, and only the result would be sent to the client. Client side scripting is processed at the client side; meaning the code would be sent to the client first, where it is eventually executed.
Server side scripting is generally applied to tasks where you don't want the end user to see the code or processed, or for tasks requiring input from the user and storage (e.g. dynamic website generation, bank programs, e-commerce, etc.). Client side scripting is used mostly for Web 2.0 applications, so that interaction would be a lot faster for the user/client.
For server side scripting, one advantage would be that the end-user won't see what algorithms are used to process the data, which is very important for secure or confidential transactions. Another advantage would be for storage of information on the server, from submissions and input of the user. The main disadvantage would be that everytime you have to process data, you need to send it back to the server before getting the result.
On the other hand, client side scripting is generally used for on-the-spot error checking, such as spelling checks and incorrect symbols, which is advantageous because unlike server side scripting, it is processed at the client itself, without any communication with the server, so it executes much faster. In the same perspective, it is also disadvantageous because the algorithm is stored in the client itself, so it poses problems especially in confidential and secure transactions.
There are lots of server side scripting languages available, such as C, C++, PHP, Ruby on Rails, Python, Perl, ASP, ASP.NET, etc. As for client side scripting languages, the ones I know of would be JavaScript, Java, Adobe Flash (or actionscrpit), Adobe Shockwave, and Silverlight (though some of these overlap with the definition of platforms).