The title says it plainly: the speaker's feelings are storms. Then the poem shows what that means by turning a weather scene into a picture of the inside of a mind. A storm haunts the house, rain runs down the walls, and lightning fills the sky. The house seems to stand for the speaker, so the storm isn't just outside. It has gotten in.
The most telling detail is the pillow, which is soaked. A pillow is where we rest or cry, so the image hints at sleeplessness or tears, though the poem never says which. The ending is the strangest and most striking part. The Darkness is capitalized and "hugging" the speaker, which is a gentle word for something frightening. It suggests the speaker feels trapped by the sadness, or perhaps has even grown used to it. The mood is heavy, tense, and lonely, but also quietly intimate.