This quote appears in chapter 1, in which Emerson briefly outlines the values of human communion with nature that he will elaborate on in the rest of the essay. He finds the solitude nature affords beneficial, and he calls it a true solitude. He also notes that nature inspires reverence, that its beauties are owned by nobody, regardless of who holds title to the land, and that most people, once they pass childhood, never really see nature. Finally and most importantly, Emerson reconnects with and becomes a "particle" of the universal godhead while communing alone with nature. Nature is where he finds the divine.
When he states that "nature always wears the colors of the spirit," he means that our response to nature is not dictated by nature itself. How we react to it is symbiotic or dependent on human mood and response. Nature paints a scene, but, Emerson says, the delight it produces emerges from "a harmony of both" nature itself and the human consciousness reacting to it.
Emerson illustrates this briefly by describing a version of what in literary thought is called the pathetic fallacy: that nature is a reflection of our own mood. How we perceive the natural world reflects the "colors" (mood) of our spirit in the sense that, for example, the same natural scene can look different based on whether we are happy or melancholy on a particular day. Just as a writer might emphasize rain to express the gloom of a character, so we, on a day we feel gloomy, might project that mood on a landscape.