Client side is when you pull all the data down and then the client segments the data into pages.
Server-side is usually done by the client providing a key that is passed to the server and then the server only selects out that "page" of data. For example if you were displaying people by last name, the first page might be created by telling the server that you want people with the last name of 'A' and that you want 10 rows returned.
The server would do something like:
SELECT ssn, fname, lname
FROM people
WHERE lname like 'a%' and rownum <= 10 ORDER BY lname, ssn;
If the last/10th record has a last name of 'abbot' with an SSN of 555555555, then the next page could be retrieved by the client passing those values back to the server which would then do something such as:
SELECT ssn, fname, lname
FROM people
WHERE lname >= 'abbot' and ssn > 555555555 and rownum <= 10 ORDER BY lname, ssn;
Server-side is considered better for large-sets of data as the amount of data transferred to the client is far smaller than if all the data is pulled down and "paged" by the client. It also lowers the memory required for the client side as well as taking advantage of the strong capabilities of databases to sort data or use existing sorted indexes to speed selection.