In the first stanza, the narrator describes the astronomer who studies the planets and stars, working to understand them on an intellectual level. He watches them and studies their movements, as carefully as if he were going to buy them, until he learns everything about them. However, there seems to be something that he is missing: the image of him "thread[ing]" the planets with his "quick-piercing mind," as one might string pearls, makes it seem like he is merely collecting knowledge without actually understanding the cosmic grandeur and beauty of the items he surveys.
The next stanza focuses on a diver who searches for an actual pearl, something that God has purposely hidden from us in order to save us from endangering ourselves in desiring it. However, the diver does risk his life only to acquire the pearl for some unnamed "her" who will wear that pearl with "excessive pride." This sin of excessive pride will lead to her "own destruction" in terms of her immortal soul. Thus, the diver endangers both himself and her in different ways.
The third stanza describes a type of scientist or doctor who is the first to come once someone has died, "Admitted to their bed-chamber, before" all of the mourners ("ordinary suitors") come to pay their respects to the dead, who will be by then "trim and dressed" for a funeral. He may "strip the creature naked" both literally and figuratively, treating the person's body as something more akin to an experiment than the remains of something spiritual and important. Again, he seems to be missing something key about life.
In the end, the narrator says, the only thing these people have found is God, whose laws have created the world around us and within us. We do not need to look so hard to try to understand what God has created by his commands; we can simply sit back and enjoy, "with love and awe," the "glorious" results of it around us. This astronomer, diver, and chymic are actually missing out on an appreciation of life.