Simple definition
A WordPress capability is a discrete permission used by roles to authorize actions.
Purpose and use
A WordPress capability represents permission for an operation such as editing a post or managing an option.
How does it work?
Roles and user permissions determine available capabilities; selected checks also consider the target object and ownership.
Example and verification
For an administrative feature, verify the required capability on the server rather than merely hiding its interface button.
Points to watch
A role name does not reveal every permission when plugins have altered capabilities. A nonce alone is not authorization.
In short
Check the actual operation and object against capabilities genuinely granted to the user.