ReadMe files should be used to describe your project and your data. When depositing data into repositories, you'll likely include a ReadMe file that just explains the files you've deposited. When you're keeping ReadMe files for your own records, it's good to have a top-folder ReadMe that explains all the subfolders and files that are part of the project as well as having them for lower-level files.
These two resources give great overviews of ReadMe files and guidance on how to create them:
via Cornell University and featuring a template!
Here's some guidance from two popular repositories that recommend and use ReadMe file:
Keep a file with information about your project in the same folder as your other files. A rule of thumb is to write as much information as necessary to understand your data.
Grateful acknowledgement to the University of Pennsylvania Penn Libraries for their permission to use and modify their template: Data Management Resources
MCW Libraries
8701 Watertown Plank Road
Milwaukee, WI 53226
(414) 955-8300