In THE FORCE AWAKENS, we have two main factions at war: THE FIRST ORDER and THE RESISTANCE. There may also be a powerful criminal organization at play that has filled the void caused by Jabba the Hutt’s death and the inability of the old GALACTIC EMPIRE and REBEL ALLIANCE to devote enough resources to maintain law and order after suffering significant losses at the Battle of Endor.
THE FIRST ORDER (bringing order out of chaos) looks to be a restructured Galactic Empire. If that is the case, it appears the Rebels and the Imperials fought to a standstill, perhaps with an armistice agreement in place. Each side now has control of part of the galaxy with a contested area between the two that has become lawless and controlled by competing criminal organizations.
Members of the Rebel Alliance who remained in the First Order’s territory (or who lived in territory recently regained by the First Order) have organized into THE RESISTANCE. The Resistance feels abandoned by the former leaders of the Rebel Alliance who failed to finish the fight against the Empire. A resistance movement almost always refers to a group in occupied territory fighting against an invader. Who knows, maybe Finn (dressed as a stormtrooper in some scenes) is actually an undercover resistance agent.
Whatever the Rebel Alliance has now become (The New Republic?), by failing to finish the fight, the First Order has been able to rebuild its forces over the last 30 years and is now ready to resume the war again.
Another possibility—and this would be a shock—is that the Rebel Alliance, unable to consolidate power and maintain order after the defeat of the Empire, formed the First Order and offered amnesty to the remaining Imperial forces if they would join them as their military/police force. This government subsequently devolved into a police state. Members of the Rebel Alliance who were opposed to this turn of events then organized into the Resistance.
Because the Empire was created through the machinations of two people, Emperor Palpatine and Darth Vader (a former Jedi), the new Rebel Alliance government feared a resurgence of the Jedi Order. Luke Skywalker fell into disfavor with the Alliance and retreated from public life into exile. Few knew of Leia’s relation to Luke, so she remained as a leader of the Rebel Alliance until she left it to lead the Resistance.