Druidism is a catch-all name for the Celtic religion. However, I feel that as a "druid" is a title and not a religion, it shouldn't be used as a tag of religious affiliation (like Catholic--you wouldn't call Catholocism "Priestism," though admittedly some--particularly the British--have called it "Papism" and "Papistry"). That being said, I'll stay within current convention and give a shorthand to what some call "druidism."
It is believed that there were three classes in Druidism; this information is based on the writings of Roman observers (Caesar, et al.), as the Celts left no religious writing.* Of these three classes, the first are said to be the Ovates or Vates, who are said to be the philosophers and seers; the Bards, who are the storytellers, singers, historians; and Druids, who are the priests and judges. It is possible (though truly unknown, despite the fanciful writings of eighteenth and nineteenth century "historians") that these were progressive grades--the first grade being the Ovate (called Faidh in Gaelic, as there is no letter "v" in Gaelic), the second being the Bard, and the third being a Druid. This is certainly how modern druid organizations are set up, but there is no way to know if this is an accurate depiction of the substructure of Celtic religious hierarchy. It is known, however, that the training to be a druid took 20 years (not unlike what it takes to earn your doctorate here in the US), starting as a young man or woman.
I say woman, as it has often been debated whether there were woman druids, or if they were lesser priestesses. However, I'm inclined to believe that there were women druids, based on an examination of Roman records, the positions of women in Celtic folktales, and the relative level of equality afforded women in Celtic society.
The druids are known to have taught metempsychosis, or the transmigration of souls--we are reborn in new bodies, sometimes human, sometimes animal. This is not a punishment, unlike in Hinduism or Buddhism, but seen as a natural part of existence. The Celts did not have a philosophy that "this world is evil and must be escaped"--far from it, if the records are to be believed. Instead, "wine, women, and song" were celebrated at all times, and being reborn was considered a good thing. The Celts were said to be unafraid of death, because of their belief in this rebirth.
*aside from Ogham inscriptions on stones, which are thought to be memorial inscriptions; and the Cologny Calendar, which is exactly as it sounds--a calendar. Caesar does say, however, that the Celts--particularly the druids--would write other matters using the Greek alphabet. Whether it was actually Greek or some derivative alphabet is not known. | 
