This important meditation on nature and the poet's son comes as the speaker finds himself in his cottage at night, watching the frost outside and with his son next to him. This quote you have cited comes from the first stanza of this poem, and is straight after the speaker has reflected on the deep silence that characterises his surroundings at night in the darkness.
The beginning of your extract is when the poet has his attention drawn to the fireplace, when he spots a film of soot fluttering on the bar of the grate of the fire. This is a "companiable form" because, in the otherwise silent and motionless night, it is the only other thing that is restless, making the speaker feel a relationship with it. This is a very important fact to focus on, because Coleridge explains in a note that such a film was often known as a "stranger," as it was said to mean the coming of a stranger or someone unexpected, which of course is used by the poet to develop his thoughts and meditation in this poem.