For a first high-level overview, please review this page on the 24Files website: How does 24Files work.
From a technical perspective:
24Files is only available for Salesforce Lightning, as it is built as a Lightning component.
24Files will create a folder structure in SharePoint at the moment the Lightning component gets loaded on the object record.
From the moment the folder structure is created in SharePoint, it is possible to manage files & folders both in SharePoint and in Salesforce (bi-directional sync).
Upon loading the 24Files component on an object record page for the first time, 24Files first searches for ‘Not-default folder structures‘ and if no ‘Not-default folder structures‘ are applicable or found, it will search for a ‘Default folder structure‘ for that object. If no ‘Default folder structure’ exists for that object, it will create a ‘Default folder structure‘. More information can be found in the section ‘24Files Folder Structures'.