The types and assignments of filtering depend on the type of clients / servers, but if we are talking about JEE, I will assume that the client is a browser and the server bean serves the facelet page.
"What exactly is filtered on the client side?"
All that can be filtered. Filtering can completely coincide with the server. This test is the so-called "protection against a fool", the purpose of which is to help the user correctly "arrange" the request.
"What exactly is being filtered on the server side?"
It is necessary to filter everything. Server-side filtering is a check that data in the correct format gets into the algorithm and, first of all, that data from the user cannot harm the server or lead to unauthorized access and any other security problems.
"What could be the goal of filtering the client side?"
First of all, reducing the load on the server (http traffic, request processing, etc.). Among the secondary reasons we can call the acceleration of validation - for example, it is not necessary to send a form and wait for an answer.
"What could be the purpose of filtering the server side?"
The guarantee that an error in obtaining incorrect data will be detected as quickly as possible (and not in the middle of the calculation process), and that the data will not compromise the security of the server.
Reference to what and how to validate (material in English).