const pointer assign to a pointer

Why can I not do this:

char* p = new char[10];

void SetString(char * const str)
{
    p = str;
}


SetString("Hello");

I have a const pointer to a char, why can I not assign the const pointer to another pointer?

It just seems illogical, as by assigning it to another pointer, you are not essentially violating the const-ness of the char pointer. Or are you?

EDIT: When I compile this it says "error C2440: '=' : cannot convert from 'char *const *__w64 ' to 'char *'"

(I'm attempting to understand a concept from a book I'm reading. Just cannot get the code to compile.

CODE:

int _tmain(int argc, _TCHAR* argv[])
{

    MyString *strg = new MyString(10);
    strg->SetString("Hello, ");

    MyString *secondstr = new MyString(7);
    secondstr->SetString("Tony");

    strg->concat(*secondstr, *strg);

}

CPP FILE:

#include "MyStringClass.h"
#include <string.h>
#include "stdafx.h"

#include "MyStringClass.h"

void MyString::concat(MyString& a, MyString& b)
{
    len = a.len + b.len;
    s = new char[len + 1];
    strcpy(s, a.s);
    strcat(s, b.s);
    delete [] s; 

}

void MyString::SetString(char * const str)
{
    s = str;
}

MyString::MyString(int n)
{
    s = new char[n+1];
    s[n+1] = '\0';
    len = n;
}

HEADER FILE:

#include <string.h>
#include <stdio.h>

class MyString
{
private:
    char* s;
    int len;
public:
    MyString(int n = 80);

    void SetString (char * const str);

    void concat (MyString& a, MyString& b);
};