The Jedi were too much on the light sight, the sith were too much on the dark side. Balance would be so called "grey" jedi, like Qui Gon Jinn, and like Luke eventually ended up as.
By killing off all Jedi and Sith, (except for Luke), you were left with one grey Jedi, thus one individual that was in balance with the force, embracing the light side, but not trying to close of his dark side. I'm guessing that when Luke started training new Jedi (which I assume he did?) he tried to teach them to be in balance of the force, unlike the jedi in the prequels.
He didn't bring balance to the force until he became Darth Vader. But techinically, he still did bring balance to the force. It makes sense to me at least 








