The speaker describes a terrible storm, or "Tempest," that churned or pounded the air. There were only a few clouds in the sky, but those clouds had a “gaunt” (or thin, haunting) appearance.
Note how, right away, the speaker subtly personifies the storm, saying that it “mashed the air” the way a person might smash something with their fist. The adjective “gaunt” is also often used to describe a person’s appearance. From the outset, then, the speaker implies that this storm has its own agency, will, and power. This storm is in fact much more powerful than any individual human being: in modern usage, the word “awful” connotes that something is terrible, but it actually means “full of awe” or awe-inspiring.
Finally, the capitalized word “Tempest” might be read as an allusion to William Shakespeare’s play The Tempest. In this play, a group of people is shipwrecked in a powerful storm (i.e., a tempest) and ends up on a remote island. A complex plot follows, but the tempest is a critical element of the play; after being washed ashore, the characters essentially lose their former identities— they are changed forever by the power of the storm.
Likewise, the poem describes this “Tempest”—a storm not unlike hurricanes often encountered in New England, where Dickinson lived—as transformative, as it will leave the speaker with a sense of awe at the intrinsic power of the natural world.