The song in my opinion is clearly a fairytale which begins with the moon and sun falling in love and all being golden (When the moon fell in love with the sun
All was golden in the sky
All was golden when the day met the night)

The next stanza talks about the moon hanging out in a garden drinking tea. The moon hadn't ever really seen the sun because she's away or just coming when he's there and when he's leaving she's coming.

(When the sun found the moon
She was drinking tea in a garden
Under the green umbrella trees
In the middle of summer
When the moon found the sun
He looked like he was barely hanging on
But her eyes saved his life
In the middle of summer)

When they finally do run into each other she's brightens the suns day because he's barely hanging on from working all the time in the middle of the summer and he wanted to meet her but didn't know how to approach her. He also didn't want anything bad to happen and so that's why he waited for her to approach him, it's his usual style. oddly enough when he met the moon it was the first time that he was able to feel the intensity of his own heat, for you see he's never had a star come that close to him before.

(In the middle of summer
All was golden in the sky
All was golden when the day met the night)

in the next stanza the sun makes his move on the moon by asking her if it would be alright if they could talk for awhile, he even promises to give her a smile. The sun works with smiles all day so he thinks maybe she came to see him smile. But she want's more, she wants to be with him and makes the sun promise not to break her heart.

(So he said, "Would it be alright
If we just sat and talked for a little while?
If, in exchange for your time, I give you this smile."
So she said, "That's okay as long as you can make a promise
Not to break my little heart
Or leave me alone in the summer.")

The sun feels overwhelmed by the moon and wants to be with her all the time but has to go to work, but then he does somethnig that he doesn't usually do, he missed work, which was just fine by the moon.

(Well he was just hanging around
Then he fell in love
He didn't know how, but he couldn't get out
In the middle of summer
All was golden in the sky
All was golden when the day met the night
In the summer
All was golden in the sky
All was golden when the day met the night)

The sun is a conservative gentleman, while the moon is a charismatic leader. The moon has everyone wanting to go see her up close but she only had eyes for the sun, which is why she went to see him. This worked out well for the sun and the moon because they both ended up falling in love.