create a vector of instances of a class in c++

The main problem is you are trying to execute a for loop at global scope. It is acceptable to define and initialize variables outside of a function, but using a for loop or assignment operator is not. Put the for loop into main() (and I would recommend you also put N and the vector/student array into main() and everything should work.
Additionally, the compiler is complaining because when you declare Student array[5]; or vector<Student> ver[N]; it is looking for a default constructor for Student called Student(), which just sets default values for a class. You need to provide this inside the Student class; set the id to some value that can never be an actual student ID, something like -1.

Option #1:

You should replace vector <Student> ver[N] with vector<Student> ver(N)

The std::vector is a class, that represents the vector by himself, you shouldn't create an array of vectors, you should just pass N(vector size) to it's constructor. Check this link

Option #2:

Student ver[N];

is incorrect, since the Default Constructor Student() is invoked N times, but you haven't implement it. So you have to use array initilizer Student ver[5] = {1, 2, 3, 4, 5} or implement the default constructor explicitly.

And of course - the "for" loop has to be used inside function body.

This:

vector <Student> ver[N];

Creates an array of N elements. Each element is vector<Student>. This is not you want. You were probably trying to create a vector of N elements. The syntax for this is:

vector <Student> ver(N);

But you can't use this because your class does not have a default constructor. So your next alternative is to initializae all the objects with the same element.

vector <Student> ver(N, Student(0));

You also tried to create an array of students like this:

Student ver[N];

This will not work. Because it tries to initialize every element in the array with the default constructor. But your class does not have a default constructor. So this will not work. But this is why your original code did work:

Student ver_list[2] = {7, 9};  // Here you are using the constructor for your object.
                               // It uses the normal constructor you provided not the default one.

The other issues is that you can not run code outside a function(method).
So this will not work:

for(unsigned int i = 0; i < N; ++i )
    ver[i].set_id(i); 

In C++11 you can initialize a vector the same way as an array:

vector<Student>  ver = { 0, 1, 2, 3, 4, 5};

If you don't have C++11 or initialization is more complex. Then you need to write a wrapper.

class VecWrapper
{
     public:
         std::vector<Student>   ver;
         VecWrapper()
         {
            ver.reserve(N);
            for(unsigned int i = 0; i < N; ++i )
                ver.push_back(Student(i));
         }
 };

Now You can place this in global scope and it will auto init.

 VecWrapper   myData;  // myData.vec  initializaed before main entered.

 int main()
 {}

Full solution:

Option 2:

#include<iostream>
#include<vector>
using namespace std;

const unsigned int N = 5;

// The following is not correct
// This creates an arrya of `N` elements each element is `vector <Student>`
//
// vector <Student> ver[N];             // Create vector with N elements
// 

// The following lines are not allowed.
// All code has to be inside a function.
//
// for(unsigned int i = 0; i < N; ++i )
// ver[i].set_id(i); 


// What you want is:
//    I use the following because it is unclear if you have C++11 or not.  
class VecWrapper
{
   public:
     std::vector<Student>   vec;
     VecWrapper()
     {
        vec.reserve(N);
        for(unsigned int i = 0; i < N; ++i )
            vec.push_back(Student(i));
     }
};
VecWrapper   myData;  // myData.vec 
int main()
{

  cout<< "Hello, This is a code to learn classes"<< endl;

  cout<< myData.vec[1].get_id() << endl;

return 0;
}