The "normal rules for name resolution" reference here is referring to the name lookup rules as they existed prior to the introduction of lexical scoping for functions. It's a dated way of describing it, as the current behaviour of functions has now been around long enough that a lot of folks will consider *that* normal, and the module, class and exec scoping rules to be the unusual case (as levkivskyi has here).

However, I've spent far too many hours staring at CPython compiler internals to be able to suggest a helpful rewording that will make sense to folks that *haven't* done that, so I'll instead provide the relevant background info to see if others can come up with a concise rewording of the reference docs :)

Prior to Python 2.1, Python didn't have closure support, and hence nested functions and classes couldn't see variables in outer scopes at all - they could see their local scope, the module globals, and the builtins. That changed with the introduction of nested scopes as a __future__ import in Python 2.1 and the default behaviour in 2.2: https://www.python.org/dev/peps/pep-0227/

As a result of that change, the compiler now keeps track of "function locals" at compile time, and *emits different code for references to them*. Where early versions of CPython only had LOAD_NAME and LOAD_GLOBAL in the bytecode, these days we now also have LOAD_FAST (function local), LOAD_CLOSURE (function local referenced as a nonlocal), LOAD_DEREF (function nonlocal) and LOAD_CLASSDEREF (class nonlocal). The latter four opcodes will *only* be emitted in a function body - they'll never be emitted for module level code (include the bodies of module level class definitions). If you attempt to reference a function local before a value has been assigned, you'll get UnboundLocalError rather than NameError.

The name lookup rules used for execution of class bodies are thus the same ones used for the exec() builtin with two namespace arguments: there is a local namespace where name assignments happen, and name lookups check the local, global and builtin namespaces in that order. The code is executed line by line, so if a name is referenced before it has been assigned locally, then it may find a global or builtin of that name. Classes that are defined inside a function may refer to lexically scoped local variables from the class body, but class variables are not themselves visible to function definitions nested inside a class scope (i.e. method definitions).

These rules are also used for module level execution and exec() with a single namespace argument, except that the local namespace and the global namespace refer to the same namespace.