This page contains spoilers.
 District 13
District 13 is the district that the Capitol destroyed at the end of the Great War.
Or so they claimed.
Throughout all the years of the Hunger Games, the districts are told that if they don't fall in line and obey the Capitol, they will be obliterated just like District 13 was. For years, the citizens of Panem believed that 13 was bombed and thus no longer existed.
It is eventually revealed that this isn't true. District 13 still exists, and was still very much alive and active with thousands of people in hiding.
 The discovery of District 13
In Catching Fire, Katniss runs into Bonnie and Twill in the woods. There, Twill informs Katniss of the upcoming rebellion and how the source of this rebellion sparks from a very alive District 13. Bonnie and Twill explain to Katniss how they know District 13 survived the war - every year, the Capitol uses video footage of the district's destruction to shove it in the faces of the nation and warn them never to fight back again. However, every year, the footage is the same. Every time, at the exact same moment in the video, a mockingjay can been seen fluttering past the Justice Building in the district. This single error, after being repeated year after year, eventually shows that the Capitol is only using the same original footage to show so-called destruction of District 13 and therefore is not showing new footage that displays what condition District 13 is actually in.
While subtle, this slip-up nonetheless shows that if the Capitol is neglecting to present up-to-date footage of District 13 and it's current condition, they must be hiding something.
At the end of Catching Fire, when Katniss is rescued from the Clock Arena in the Quarter Quell by hovercraft, it is revealed that Bonnie and Twill's suspicions were correct. She learns that it is true that District 13 exists and plays a significant role in the second war against the Capitol.
 General District 13 Information
District 13's primary industry was the production of nuclear weapons.
 Structure and History of District 13
The president of District 13 is Alma Coin.
District 13 resides entirely underground. After it was bombed many years ago, the remaining living citizens fled to the only place they could avoid the radiation - beneath the earth. It was here that they re-built their district by constructing multiple living compartments, a hospital, a Command Center, and a massive cafeteria where they all would eat together.
District 13 requires its citizens to all wear the same grey outfits, and they all must also wear tracking bracelets on their wrists. Each resident is assigned a daily schedule that is imprinted on their arm every morning and they must abide by their designated schedule.
District 13 is also essentially a military grounds. Their primary focus is to become strong enough to overpower the Capitol and so, above the land, they have what are called training grounds, and when a child reaches a certain age, they are expected to begin attending training sessions that prepare them to fight in a war. As such, these children are referred to as soldiers and hold a higher status of respect.
Resources run low in District 13, therefore there are many rules regarding the usage of these resources. Food served is typically cheap, bland and unappealing, and portions are drastically restricted. In fact, food portions are so highly restricted that if one is caught stealing or sneaking in more than they are meant to be served, severe (and often cruel) punishments are enacted.
 Citizens of District 13
Some of the people who reside in District 13 are: