“There’s no one better to quiet a horse. I lay my big hands on them, and feel them trembling—I know how they feel. They’re like me: big and timid. So I breathe sweet peace to them—not with my lips, but through my fingers—and they hear me, not with their ears but through their skins.”
The author writes the phrase “I breathe sweet peace to them—not with my lips, but through my fingers—and they hear me.” What does she mean?

Please help me I'm going to fail T-T