The Book of Nature is part of a philosophy that Christians have historically had concerning the natural world. All things come from a single source: God. Understanding of those things comes from the study of two things: the Bible, and the Book of Nature.
This concept became particularly important around the time of the Renaissance, when Christians were rediscovering and embracing the writings of ancient Greece and Rome, many of which emphasized the study of the natural world.
Those who studied what we today would call science were commonly described as natural philosophers. This was a term applied to such well known intellectuals as Galileo Galilei, Sir Isaac Newton, and other important figures of the Scientific Revolution.
Religion and science were not completely separate fields of thought until very recently. While proto-scientists sought to understand the physical world through physical principles (rather than simply consider it the will of God), it was still understood that God put such principles into motion. Understanding the creation helps one to better understand the creator.
The Book of Nature was created by God to be read by humanity. The natural philosophers saw no reason why God would put forth knowledge if he didn't want anyone to learn about it. However, much of that knowledge was hidden, which is the literal meaning of the word "occult." Seeking out this hidden knowledge was the occupation of the astrologers, the alchemists and other occultists, who studied this knowledge through investigations into physics, chemistry, astronomy, botany, medicine, and so forth.
Studying this knowledge was considered the prerogative of intellectuals. Scripture contained the obvious messages for all of humanity. However, the Book of Nature was more subtle. Thus, it was suggested, its secrets were more likely to be abused by those who couldn't properly appreciate them. It is one reason why occultists often wrote in code and described their ideas in complicated language, hoping only understandable by those as highly educated as they.
Having knowledge of God meant becoming closer to God and vice versa. This meant those who studied the Book of Nature were expected to be spiritual people. A person of low morals would not be able to properly understand the lessons of the Book, although he might misunderstand it and cause harm through his ignorance.
Alchemy is perhaps the most obvious branch of study to focus on spirituality. The idea of transforming lead into gold is metaphorical. The ultimate goal of alchemy has always been to take something coarse and common - the average human soul - and transform it into something more pure, more spiritual, closer to God. Alchemy is about enlightenment and spiritual evolution, but it was approached through partially though the language and study of chemical interactions.