Born in Esens, Frisia, as an adult David Fabricius (a Latinized version of his proper name David Faber) served as pastor for small towns in Frisia (part of modern-day Germany). As was common for churchmen in those days he dabbled in science; in his particular case the science was astronomy.
Fabricius made his first mark on history by discovering the first known periodic variable star (as opposed to cataclysmic variables, such as novas and supernovas), Mira, in August of 1596. At first he believed it to be "just" another nova, as the whole concept of a recurring variable did not exist at the time. When he saw Mira brighten again in 1609, however, it became clear that a new kind of object had been discovered in the sky.
Two years later, his son Johannes Fabricius returned from university in the Netherlands with telescopes that they turned on the Sun. Despite the difficulties of observing the sun directly, they noted the existence of sunspots, the first confirmed instance of their observation (though unclear statements in East Asian annals suggest that Chinese astronomers may have discovered them with the naked eye previously, and Fabricius may have noticed them himself without a telescope a few years before). The pair soon invented camera obscura telescopy so as to save their eyes and get a better view of the solar disk, and observed that the spots moved. They would appear on the eastern edge of the disk, steadily move to the western edge, disappear, then reappear at the east again after the passage of the same amount of time that it had taken for it to cross the disk in the first place.
This suggested that the Sun rotated on its axis, which had been postulated before but never backed up with evidence. Johannes published Maculis in Sole Observatis, et Apparente earum cum Sole Conversione Narratio ("Narration on Spots Observed on the Sun and their Apparent Rotation with the Sun") in June of 1611. Unfortunately, the book remained obscure and was eclipsed (so to speak) by the independent discoveries of and publications about sunspots by Christoph Scheiner in January 1612 and Galileo Galilei in March 1612.
Besides these two discoveries, little else is known about David Fabricius except his unusual manner of death: after denouncing a local goose thief from the pulpit, the accused man struck him in the head with a shovel and killed him. Copies of a map he made of Frisia in 1589 are also still extant. He is also name-checked in Jules Verne's From the Earth to the Moon as someone who claimed to have seen lunar inhabitants through his telescope, though that particular fact is merely part of Verne's fiction.
A large (90 kilometer) crater on the Moon's southern hemisphere has been named Fabricius, though whether after the father or son is unclear.