Agrippa's organisation is the reason the work mattered, and it is visible in the title of each book. The first treats natural magic, the world of the elements: the occult virtues of stones, plants, animals and metals, the doctrine of sympathies and antipathies, and what a practitioner can do by manipulating them. The second treats celestial magic, the world of the heavens: number, proportion, harmony, the planetary tables and seals that the atlas records under planetary magic, and the making of images under the stars. The third treats ceremonial magic, the intellectual world: divine names, angelic hierarchies, the soul's ascent, and religious rite.
That threefold ascent from matter through number to spirit is a Neoplatonic scheme, and by arranging the material inside it Agrippa turned a mass of inherited technique into something that could be presented as a philosophy. Every later Western ceremonial system inherits the architecture, whether or not it inherits the contents.
The books were written around 1510 and printed in 1531 and 1533, and the twenty year gap matters: Agrippa published in between a work arguing the vanity of all the sciences, including this one, and readers have argued ever since about which position he held.