How exactly stdin, stdout, stderr are implemented in linux?
stdin, stderr, and stdout are file descriptors (or FILE* wrappers around them, if you mean the C stdio objects bearing those names). File descriptors are numbers that index a per-process data structure in the kernel. That data structure records which I/O channels a process has open, I/O channel being my ad-hoc term for a file, device, socket, or pipe.
By convention, the first entry in the table has index 0 and is called the standard input, 1 is the standard output and 2 is the standard error channel. This is just a convention in Unix programs; as far as the kernel is concerned, nothing's special about these numbers.
Each I/O system call (read, write, etc.) takes a file descriptor that indicates which channel the call should operate on.