Explanation of std::function

Question

What is the purpose of std::function? As far as I understand, std::function turns a function, functor, or lambda into a function object.

I

Answer 1

Consider a simple use case:

/* Unspecified */ f = [](int x, int y){ return x + y; };
f = [](int x, int y){ return x - y; };
int a = 42;
f = [&a](int x, int y){ return a * x * y; };

How would you specify /* Unspecified */?

Furthermore,

std::queue jobs;
jobs.push_back([]{ std::cout << "Hi!\n"; });
jobs.push_back([]{ std::cout << "Bye!\n"; });
for(auto const &j: jobs) j();

What value_type should be kept in jobs?

Finally,

myButton.onClick(f);

What type does f have? A template parameter? Okay, but how is it registered internally?