Since implementing caching manifests would not be sufficient in itself to create an application to work wholly offline (such as outlined in bug 28706), this step would be for the sake of improving performance and lowering demand on the server, but could facilitate any future steps toward caching content as well.
After the first time obtaining copies of such resource files, browsers would never need to ask Wikipedia again for new copies, except for occasionally pinging Wikimedia servers (when online) to check whether there were any updates to those files that needed to be auto-downloaded.
Browsers of course currently do cache Wikipedia files, but they don't reserve permanent space in the browser for these files, so the browser will periodically need to re-download these files and thus slow down their visits and demand on the server.
Browsers may impose size limits on the amount of memory that can be used by a given domain for resource file caching, or require permission when beyond a specific size, so the user experience or availability may differ slightly based on the browser.
Documentation on manifests are here: http://www.whatwg.org/specs/web-apps/current-work/multipage/offline.html