Herbaceous plants are plants with non-woody stems. Their above-ground growth usually dies back in winter in the temperate zone, even in cases where the plants in question are perennials. All "annual" plants are "herbaceous," but not all herbaceous plants are annuals. An "annual" is a plant that dies altogether at the end of the growing season, both above the ground and below it. "Perennials," by contrast, survive the winter, even if their above-ground growth dies back.
Usually, when people speak of "herbaceous" plants, they mean perennials such as peonies and bearded iris. The term thus applied enables us to distinguish such plants from other groups that are, technically, perennial: namely, the trees and shrubs. The latter can be classified as woody perennials, although they are more commonly treated as distinct groups.