What are Temporary Internet Files and why would one want to keep them?
If they are not needed how do I stop users in a citrix environment from saving them?
This is not a term that means only one thing. You need to start by finding out what application is using this term, and find the documentation for this application or other information about it that explains how they're using that phrase. The context of the phrase could be relevant also, such as was it seen in a directory name, in a dialog, in a menu option, etc. And obviously what other words were surrounding it, if it was part of a question, or what exact menu this option was seen in.
Microsoft has a page documenting it http://support.microsoft.com/kb/260897, and there's a wikipedia page describing it http://en.wikipedia.org/wiki/Temporary%5FInternet%5FFiles.
I would say those provide a reasonable guess as to what you've want, but I assume you've already seen the first screenful of google results. So some more information is probably necessary in determining what the actual question is.
The context where I've most often seen the general term "temporary internet files" used is with web browser caching.
Most web browsers can be configured within the browser to set the number of cached pages they save. These are used to serve a page a user goes back to from the local cache, which is much quicker than going back out to get a new page.