The C++ specification on what exactly an STL container is mandates that any STL container type have several different fields available. Some, like begin() and end(), are functions, while others, like iterator, are types. These restrictions also apply to iterators. This allows C++ template functions to introspect on their types of their arguments to look up more properties. For example, all STL iterator types must define an iterator_category field containing a type encoding their capabilities. This way, the STL algorithms can have different implementations of different functions based on the power of the iterators they accept. A class example is the distance function, which takes two iterators and returns the number of spaces between them. If the input is a lowly ForwardIterator or BidirectionalIterator this works by marching the iterators forward and counting how many steps were took, which runs in O(n). If the input is a RandomAccessIterator, then the iterators can just be subtracted to get the result in O(1).
Prior to C++17, the recommendation was to include the <iterator> header and inherit from std::iterator to automatically generate the necessary nested types you’d need (reference, pointer, etc.). That type is now deprecated, and so you’ll need to manually either add typedefs or specialize std::iterator_traits to export this information.
As for what operators you need to overload, at a bare minimum you need to get ++ (prefix and postfix), ==, !=, * (pointer dereference), and -> defined. All iterator types support this. For bidirectional iterators or higher, you should also have -- defined (prefix and postfix). Finally, for random-access iterators, you should support [], +, +=, - (back up many steps and subtract two iterators), -=, <, >, <=, and >=.
Hope this helps!