for using cout, I need to specify both:

#include<iostream>

and

using namespace std;

Where is cout defined? in iostream, correct? So, it is that iostream itself is there in namespace std?

What is the meaning of both the statements with respect to using cout?

I am confused why we need to include them both.

iostream is the name of the file where cout is defined. On the other hand, std is a namespace, equivalent (in some sense) to Java's package.

cout is an instance defined in the iostream file, inside the std namespace.

There could exist another cout instance, in another namespace. So to indicate that you want to use the cout instance from the std namespace, you should write

std::cout, indicating the scope.

std::cout<<"Hello world"<<std::endl;

To avoid the std:: everywhere, you can use the using clause.

cout<<"Hello world"<<endl;

They are two different things. One indicates scope, the other does the actual inclusion of cout.

In response to your comment

Imagine that in iostream two instances named cout exist, in different namespaces:

namespace std{
   ostream cout;
}
namespace other{
   float cout;//instance of another type.
}

After including <iostream>, you'd still need to specify the namespace. The #include statement doesn't say "Hey, use the cout in std::". That's what using is for, to specify the scope.