Azarath in the animated series
Azarath is the extra-dimensional birth world/realm of Raven. Her mother, Arella, was brought here from Gotham City (under her birth-name, Angela Roth) to hide from Trigon's evil and to shield her only daughter as best she could. It was a peaceful dimension where its residents were taught pacifism, led by their leader Azar, who led the order that originally sealed Trigon into his prison.
Raven invokes the name of Azarath in her chants to summon and focus her dark powers and abilities (Azarath, Metrion, Zinthos). Apparently it serves as at least one source of her power, as implied when David Slack commented "Whenever Raven was in trouble, she called on the power of Azarath; So when Raven is in the greatest trouble of her life, it seemed like we should take her to Azarath. Raven left this peaceful society in an attempt to repent in advance for the terrible fate that she would eventually bring to the world." However, for some reason Raven was shown to use her old invocation and was able to evidently use it to evoke power even after the apparent destruction of Azarath at least once afterwards, before Slade assaulted Titans Tower.
An example of Azarath architecture
In the episode "Switched" of the first season, Raven tells Starfire that she was born in a place called Azarath, but Raven does not specify that she, in fact, lived there (Although considering that this was followed by a transition to the next scene, she may have said so off screen)
During the fourth season, Raven visits Azarath, in the episode "The Prophecy," to seek help from her mother, Arella. It is protected with a mystical seal warding away all intruders, but Raven used her powers to penetrate it and the chakra jewel on her forehead began to glow red. However, the temple-city is deserted and is later revealed to be an illusion left behind after Trigon supposedly destroyed it. With Azarath having fallen to Trigon's rule and Azar and her ancient order no more, Earth is left nearly defenseless against an open invasion by Trigon.
In Teen Titans Go!, Azarath is restored, with Raven telling Arella she has cleansed Trigon's stain from both worlds.
Arella refers once to the citizen's of Azarath as "[Raven's] people"; many believe this to be an implication that the two are seen as some form of nobility, but there has never been any confirmation of this.
The Seal of Azarath