The Big-O notation defines the time complexity of...
A specific problem, as for example, the Element Uniqueness in an Array.
A specific algorithm, as for example, the Brute Force implementation of the Element Uniqueness in an Array.
A specific execution of an implementation, as for example, when you run the code with the nested loops in the Python code for the Brute Force implementation of the Element Uniqueness in an Array.
A specific implementation, as for example, the nested loops in the Python code for the Brute Force implementation of the Element Uniqueness in an Array. (That is to say, a different implementation of precisely the same algorithm/approach for a problem could have a different Big-O class in say C++ or Java.)