The phrase "under the covers" is being used metaphorically. There are two common literal meanings of "under the covers":
- The insides of a piece of machinery, which are covered by a removable "hood" or "cover". A closed hood makes it harder for the user to accidentally hurt themselves or damage the machine.
- Being in bed, under sheets and/or blankets. Sheets and blankets are layers of "covers".
In computer programming, the purpose of a "programming library" is to provide easy-to use features, without the user needing to worry about the details of how the features are implemented. This also avoids bugs: If the user never works with the details, the user cannot make a mistake by mis-using the details. These "hidden details" are "under the covers".