In the first stanza, we're looking down on a man in the street as the moon shines down on him. Where's the Man-Moth? Oh, there he is in the second stanza, coming out from under the streets. He's kind of twitchy about being up here. He believes the moon is a hole in the sky, and he's trying to get up to see what's on the other side. He's still nervous and afraid, but he paints a dramatic picture as he scales up the buildings. He's like if Spiderman and Batman adopted a giant moth. Turns out he's no Spiderman or Batman (he was adopted after all), though, because he falls, and this seems to be the usual course of events when he tries this.
We follow the Man-Moth underground in the second part of the poem and hop on a subway train with him. He does odd things like insisting on sitting backward and never taking his hands out of his pockets, seeming very alien even though this is his home.
In the end, we're encouraged to take a closer look. The good news is that he doesn't seem to mind if you shine a flashlight in his eyes. In fact, if you do it, he'll give you something precious—a single tear—if you pay close enough attention. The meaning of all of these things depends on how we interpret what's going on.