The movie doesn't do a very good job of explaining it, but I don't think it's that hard to conceive of:
After the events of ROTJ, the overall regime that administered the state [The Empire] collapsed and was taken over by the Rebellion, re-forming as a new Republic. After which the [still heavily armed] loyalists of The Empire re-consolidated their power in a significant amount of territory to form a new state, The First Order. The Republic and the First Order were then locked in a sort of cold war, where both sides made ostensible military concessions to prevent another full scale war. Amidst this "peace," The Resistance popped up to challenge the First Order within its own territory. The Resistance, while officially independent of the Republic, is clearly composed of key members of its founding organization (the Rebel Alliance), which likely makes diplomatic relations between the Republic and the First Order all the more shaky. This is the political situation leading into The Force Awakens.