That is because you are concatinate two string literals, which is not neccessary here. Note that you do not need "windows.h". You do need <string> when you work with strings though.
system takes a const char* as input, so you need to call the string function that returns such a pointer.
Code:
#include <iostream>
#include <string>
int main()
{
std::string Message;
std::string Recipient;
std::string Command;
std::cout << "Please enter your message:";
std::cin >> Message;
std::cout << "Please enter the recipient:";
std::cin >> Recipient;
Command = "msg.exe " + Recipient + " " + Message;
system( Command.c_str() );
std::cin.get();
return 0;
}