1) Chantry
2) Templar
3) Mage
4) Inquisition
Also, one other question: So in this game in order to progress I have to use the War Table? Or can I just run outside of town and keep walking?
1. The Chantry is the organization founded around the Chant of Light, which is the major religion in Thedas revolving around the Maker and his favorite human female Andraste, and it teaches a many things about the creation of existence as the people of Thedas understand it, and it is historically correct about some of those things.
2. Templars are warriors who train in anti-magic and take lyrium to help them deny/nullify magical energy, and because of this ability they are tasked by the Chantry to watch over mages to protect the people from magic and slay any mage who is possessed by a demon.
3. Mages are born with the ability to use mana to create magical effects in the real world, they usually discover their abilities during childhood, and they are usually sent to Circles where they learn to control their magic and resist possession by spirits that target mages specifically because of their close connection with the Fade.
4. The Inquisition began some 800 years ago as an organization that hunted down dangerous mages and demons to slay them, but they eventually pledged themselves to the Chantry, splitting into Templars who watched the mages, and Seekers who watched the templars to make sure they were performing their duties as directed, until the present day when they were called upon to close the Breach, find those responsible, and restore order.
You must use the table to open up new quests and new maps.
Another thing you should know is that the Fade is a parallel world to the real world made of magical energy which is shaped by thought and his home to countless spirits and demons.
Also, the Darkspawn taint is a curse unleashed by ancient Tevinter mages who entered the Golden City in the Fade and brought the curse back with them to the real world.