Describe what assignment day is in The City of Ember.

In the novel The City of Ember, Assignment Day is the day kids graduate from their schooling. At the end of their education, they are assigned a job, which they must report to regardless of their preference. These jobs are essentially doled out at random, and many people end up in fields they don't care for.
The two main characters, Lina and Doon, are assigned jobs as Pipeworks Laborer and Messenger, respectively, but neither of them like their particular assignments. So, the two switch, which sets off the events of the novel. This "assignment" trend is similar to many other dystopian or youth fiction novels, where characters are sorted or divided and put into specialized groups essentially against their will, like in Harry Potter, the Divergent Series, and other books.