what does it mean? it means Luke will die.
as the movie begins, it refers to "Luke The Last Jedi", as this WILL be a movie about luke.. but when the movie is over, then the Last Jedi will be Rey.
she is the center of the trilogy, afterall. The Force Awakens in HER. the last jedi is HER.
when the movie is over, there will be no jedi at all.
ie: the words "Star Wars" are done in red. why red?
--> Rey will turn. Luke will be the last jedi, because his padawan becomes a sith. and yea .. he dies. either way. "last jedi" and all that.
(they revealed the ending by this title : either way , Luke dies --- either Luke is, in fact, the "Last Jedi" (which means there will be no more after him, he will die, and take the JEdi Order with him to the grave, thus becoming the Last Jedi Ever) ; or Rey becomes the "last jedi" by the end of the movie (which means: Luke is dead, either way).