"The moisture of the earth, which the sun attracts by his rays, he again parts with ..."

 The "moisture of the earth" refers to the "waters," the deoxygenated blood coursing through the p. arteries and its branches towards the final end point, the alveolar region. These arteries and branches run alongside the "rays of the sun," the bronchi. Poetically speaking, the sun, by means of its rays, is sucking up the waters, the moisture. The waters are, as it were, being pulled towards the sun or attracted by its rays. 

These waters or moisture of the earth is again released, as it were, by the sun--its rays--at the level of the alveoli. The deoxygenated blood is reoxygenated and released as most pure "rain" into the "crops" and the "plants," the (venous) capillaries. This is on the side of the p. venous network. The p. vein is also known as the "moon," and therefore it is said that the waters are transmitted to the moon. 

The poet-anatomist is viewing the sun or the bronchial network as the agent that mediates the transformation of the "waters." The p. arterial flow (deoxygenated) transforms into the p. venous (oxygenated) flow due to the activity of the sun (the bronchi and the alveoli). This physiological role is highlighted. 

Or, perhaps it's once again an ingenious innovation of our poet-anatomist to highlight the difference between the conducting and the functional zones of the lung. The acinus is the productive zone; it's fertile and it's supposed to rain here so that "food" may be produced; in contrast to the higher (conducting) zones where the rain or the waters are merely to be guided and conducted (towards the acinus).