std::function is designed to represent any kind of callable object. There are plenty of callable objects that cannot be represented in any way by a function pointer.
A functor:
struct foo {
bool operator()(int x) { return x > 5; }
};
bool (*f1)(int) = foo(); // Error
std::function f2 = foo(); // Okay
You cannot create an instance of foo and store it in a bool(*)(int) function pointer.
A lambda with a lambda-capture:
bool (*f1)(int) = [&](int x) { return x > y; }; // Error
std::function f2 = [&](int x) { return x > y; }; // Okay
However, a lambda without a capture can be converted to a function pointer:
The closure type for a lambda-expression with no lambda-capture has a public non-virtual non-explicit const conversion function to pointer to function having the same parameter and return types as the closure type’s function call operator. The value returned by this conversion function shall be the address of a function that, when invoked, has the same effect as invoking the closure type’s function call operator.
Implementation-defined callable return values:
bool foo(int x, int y) { return x > y; };
bool (*f1)(int) = std::bind(&foo, std::placeholders::_1, 5); // Error (probably)
std::function f2 = std::bind(&foo, std::placeholders::_1, 5); // Okay
std::bind's return value is an implementation-defined callable object. Only how that object may be used is specified by the standard, not its type.