The City Of Ember (later unofficially renamed Darkhold) was an underground city created to protect humanity from a nuclear/biological war for at least 200 years. However, it held the inhabitants for around 241 years. Ember is entirely underground. It is where the first book, City of Ember, takes place.
The first inhabitants were 100 infants and 100 adults - 50 men and 50 women. The adults were all age 60 or older and were instructed to bring no books or photographs from the outside in with them. They were to raise the children as their own.
A titanium box was left in the care of the first mayor. It contained the instructions for leaving Ember when it automatically opened in 200 years, which is when it was assumed that it would be safe to leave
The city is likely called "Ember" because it maintains and protects the last remnants of humanity, in a state much like the embers of a fire. This is hinted in The People of Sparks, where Maddy tells Lina that Sparks is a place that is just starting out, much like how sparks are the start of a fire. It is probably also a reference to the fact that Ember is "the only light in a dark world", as it was a city surrounded entirely by darkness, much like an ember in the night.
The first book revealed that there are certain celebrations in Ember, such as the Singing, where the citizens sing three songs that are much like the anthems of Ember. The songs sung are "Song of the River", "Song of the City", and "Song of Darkness." Each song has an accompanying banner as well. A spiritual group called the Believers often lead the Singing, and believe that the Builders will eventually return and rescue them. Their ideology became more popular as Ember's power and food supply drained.
Another special day in Ember is Assignment Day, when the twelve-year-old students of the highest class are assigned a job by picking a slip of paper with a job written on it out of a bag.
There was mention of something called The Cloving Square Dance Day, although this seems to be a one-time event.
Upon the death of an individual, friends and family take the body beyond the Trash Heaps, sing "The Song of Goodbye," and abandon the body to decomposition.