Particularly pertaining to the Parse platform, 'CLPs' are Class-Level Permissions on the database which dictate who can do what with a given class. Actually, they only dictate public permissions — whether or not anyone can get, find, create, update or delete some class.
ACLs (Access Control Lists) are more granular. They exist on a per-record basis dictating who can do what. Assuming the CLP on a class for a given operation, say 'update', is public, the ACL can overwrite it — only allow certain users to update it, enable anyone to update it, etc.
However, if the CLP for the 'update' operation doesn't allow public access, the ACL cannot overwrite it.