The speaker of the poem watches a spider on a "promontory" as it explores its surroundings through sending out huge numbers of filaments on every side to give itself a sense of where it is in relation to everything else around it. The speaker notes that the spider does this endlessly and tirelessly.
In the second stanza the speaker uses the sight of this spider and his action as a metaphor to describe his own soul. Just as the spider is surrounded by lots of space, so his soul is surrounded by "measureless open space." His soul therefore casts out endless filaments as well, "seeking the spheres, to connect them." The aim of the soul, the speaker suggests, is to try and connect itself to the sense of the divine:
Till the gossamer thread you fling, catch somewhere, O my Soul.
The poem is therefore about loneliness and also the search for meaning and a sense of the divine in a world where it is so easy to become overwhelmed by the space around us.