Server side is all the info that has your server, like the database (which has all the monsters), the jobs info, the maps, etc... You update this to get the new content on your server and only once every now and then.
The client side has the information about the way the server is shown in your pc, like the buttons, new GUI, new images when loading, new patcher, etc... You update this because the new content on your server needs to be shown by the client and the client has the info about how to do it like the translations (in this case).
This is overall how I see it, but you can check the https://rathena.org/board/forum/98-client-side/ forum to see more or less what else you can do.