A few years after RotJ Luke established a new Jedi Academy to begin reconstituting the Jedi ranks. Two of his first padawans were Han and Leia's twin children, a boy and a girl.
In the wake of the collapse of the Empire into various factions ruled by different Moffs, the surviving dark side adepts, Sith acolytes, and Emperor's Hands were united into the Knights of Ren by the most powerful among them, a being named Snoke. They threw their lot in with the most powerful of the surviving Moffs and through their combined strength they were able to bring the other former Imperial factions into line, thus establishing the First Order out in the Unknown Regions as an opposition force to the fledgling New Republic.
The New Republic was overwhelmed dealing with establishing itself and providing for a galaxy still recovering from the Galactic Civil War, so they unfortunately allowed the First Order to grow like a cancer under their own nose. Only a few of their leaders were prescient enough to recognize the danger if the First Order expanded in the Outer Rim. Princess (now General) Leia and Han Solo formed the Resistance, a new rebellion made up of the few New Republic volunteers not weary of war and citizens from the systems conquered or threatened by the First Order. Luke offered the assistance of some of his more experienced padawans.
Realizing that they faced a new threat to their existence, Lord Snoke and General Hux decided to deal a devastating blow to the leaders of this new Resistance and their Jedi allies. They attacked the Jedi Academy on Yavin IV, killing many trainees and teachers and attempting to kidnap Leia and Han's children. Luke was able to protect the girl, Rey, but Snoke kidnapped the boy to train as his own apprentice, now renamed Kylo Ren.
Devastated by his failure to prevent the destruction of the Academy and protect his apprentices and family, Luke went off into exile, seeking to commune with the Force and find a way to defeat this new threat of the Knights of Ren and clarify visions he's seen of a new superweapon that can destroy entire star systems. He's foreseen that his time will come to return either when his niece Rey seek him out in exile to train her once again, or his nephew Kylo shows up to destroy him. Luke hopes to turn Kylo back to the Light like he did his father.
Han, angry and seeking vengeance, leaves in a New Republic Star Destroyer to search for his son.
Leia, unable to leave her duties as leader of the Resistance and go on the search with Han, turns Rey over to a trusted confidant of hers living on the planet Jakku, knowing that she'll never be safe as long as the Knights of Ren know she's with Leia. She tells Rey not to develop her Force abilities for fear that it would attract too much attention.
Kylo Ren, twisted to the dark side by Snoke, learns of his grandfather Darth Vader, and aspires to finish his task of destroying the Jedi, including his own uncle Luke.