The best-known Hermetic sentence is not from the Corpus Hermeticum. It comes from the Emerald Tablet, a short text first attested in Arabic in about the eighth or ninth century and translated into Latin in the twelfth, which opens with the statement that what is below corresponds to what is above, and what is above to what is below, in the accomplishment of the miracle of the one thing. In Latin Europe this became the motto of an entire way of thinking.
The idea it compresses is correspondence: the cosmos is a single connected order in which the human being is a microcosm answering to the macrocosm, so that metals answer to planets, plants and stones to signs, and organs of the body to regions of the sky. If the correspondences are real, they can be worked with. This is the theoretical ground beneath astrological medicine, talismanic magic and much of alchemy, and it explains why those practices were not regarded by their practitioners as arbitrary but as applied cosmology.
The philosophical dialogues are less concerned with technique. Their subject is the ascent and destiny of Nous, mind, which is of divine origin and capable of returning to its source. The human being is described in the Asclepius as a great wonder, positioned between the divine and the material and belonging to both. Salvation is by knowledge, and the ascent is often described as the shedding of the qualities acquired from each planetary sphere on the way down: as the soul rises it returns growth-hunger to one sphere, guile to another, ambition to a third, until it stands free.
Where Hermetic writing differs from the gnostic material it resembles is in its attitude to the world. The gnostic scheme generally treats the cosmos as a prison built by an inferior maker. The Hermetic texts more often treat it as beautiful, ordered, and itself a revelation of god, describing the cosmos as a second god and the visible order as something to be contemplated rather than escaped. They are not consistent about this, and some passages are bleakly dualist, but the dominant tone is affirmative, and that difference is why Renaissance readers found the literature so usable.
Alchemy absorbed the vocabulary wholesale. The word hermetic in the sense of sealed comes from a laboratory technique attributed to Hermes, and the language of the tradition has been embedded in Western esoteric practice ever since.