Something all the writer's I admire have, is what I call a "song instinct". By that, I mean that they can hear and nurture a song inside themselves. It sounds complete to them and they know it will resonate with others.
The most famous example I can think of, is the discovery of the melody of "Yesterday", by Paul MacCartney. He tells the story of how he heard it in a dream and he kept asking people if they knew where it was from. He knew it was a good song.
The part which forms the backbone of that melody is interesting too. It starts in C and then moves to an E major chord. Most of us would have automatically played an E minor. Macca was able to hear the shape of a melody on a simple, but slightly modified chord progression. The clever part was the instant recognition that this would form an original yet exceptionally accessible melody. The words are simple, but they scan perfectly. He tells you just enough to put you in his shoes.
I asm only repeating what others have said before me here, but it is that marriage of craft to pure instinct which gives reise to the greastest of songs.