What exactly is One Definition Rule in C++?

The truth is in the standard (3.2 One definition rule) :

No translation unit shall contain more than one definition of any variable, function, class type, enumeration type or template.

[...]

Every program shall contain exactly one definition of every non-inline function or object that is used in that program; no diagnostic required. The definition can appear explicitly in the program, it can be found in the standard or a user-defined library, or (when appropriate) it is implicitly defined (see 12.1, 12.4 and 12.8). An inline function shall be defined in every translation unit in which it is used.