The first time the narrator of the poem describes a hug, one she shares with her companion while they have stopped to listen to a woman reading a poem in the street, she describes it as being
[. . .] like a variable star shooting light off to make itself comfortable,
To the speaker, a hug is something much more significant than a simple physical embrace. To her, it seems like something on the scale of the cosmos; it is huge, like a star that is so brimming with light that it must "shoot" some off in order to feel more comfortable. Perhaps the speaker is so brimming with love that she must release some of it via the hug to her companion.
This feeling may account for the speaker's surprise when her companion is so willing to share her and her meaningful hugs with a strange man, perhaps a homeless man, who looks on. She does go and offer this man the hug he has requested, and even as she is asking herself how long the hug should last or how big it should be, she thinks,
Already we could be eternal,
His arms falling over my shoulders, my hands not meeting behind his back, he is so big!
She continues to use the language of cosmic significance when describing even this hug with a stranger by suggesting that they might be "eternal." Her attempt to connect with another human being feels so important that she compares it to abstractions—or, rather, things that are so huge that they seem abstract and unknowable. She even suggests that she and he have "stop[ped] having arms."
In the end, the speaker knows that this hug is going to leave a lasting impact on her life. She says that a hug ought to be a
masterpiece of connection, the way the button on his coat
will leave the imprint of a planet in my cheek when I walk away.
Certainly, we can understand how a button pressed into a cheek would leave a small physical mark, but because the speaker describes it as a "planet," she seems to suggest that it will be much more than merely small and physical. This hug will have a lasting emotional impact on her life as well, as she seems to believe that all good hugs should do.