Prior to FileMaker 13 we never even had the option of performing scripted tasks where the data actually exists. The processing of a script, client side, always had, and still does, make a full round trip for all kinds of these processing activities. Many times, FileMaker does it's best to optimize whatever is being done, but it's still not as fast as executing certain things directly on the server.
With the addition of Perform Script on Server we gained a REALLY BIG performance boost by being able to perform most any script on the server.
While there are still various limitations, such as the number of simultaneous server side scripts, it's absolutely something that any serious FileMaker developer needs to know how to use.
One of the biggest issues with running server side scripts with Perform Script on Server is the fact that you need to know what's happening when the script is running, how to troubleshoot and most importantly, how to replicate the current user context. That is, the proper layout and the exact same found set to be used for processing the data. This video specifically covers how to restore the user context for processing a found set of data. If you're interested in making this process happen as quickly as possible, then using Perform Script on Server is what you should learn to use.
Click the title or link to this article to view the video.