Public API refers to the “point of access” that the external world (users, other programs and/or programmers, etc) have to your software.
E.g., if you’re developing a library, the public API is the set of all the methods invokations that can be made to your library.
There is understanding that, unless a major version changes, your API will be backwards-compatible, i.e. all the calls that were valid on a version will be valid on a later version.
You can read at point 9 of those rules:
Major version X (X.y.z | X > 0) MUST be incremented if any backwards incompatible changes are introduced to the public API.