FORMAT does not send a string to a file. It executes a program in a domain specific language which creates output to a stream. This does a bunch of operations

FORMAT does not send a string to a file. It executes a program in a domain specific language which creates output to a stream. This does a bunch of operations. The print functions are being executed on an output stream. If the ARG is NIL, then FORMAT creates a string output stream and later returns the generated string. (format nil "~a" 3) is just short for: (with-output-to-string (stream) (format stream "~a" 3)) ~a is then an operation which writes the argument 3 to the output stream.