"Server side" refers to the part of a computer program that runs on the server, rather than on the user's device. It handles requests from the user and processes data or performs tasks, then sends the results back to the user. Full definition
The traditional security model has focused on server side security which puts large third parties in control the most sensitive data, this is security at the «center» of the network. (cryptoninjas.net)
Detailed packet analysis and inference on what the code looks like server side in order for some of the exploits to be possible is presented. (defcon.org)
Characters are being stored server side like a MMO. (reddit.com)