Star Wars: The Last Jedi Trailer Breakdown: 21 Things You Need To See
14. Lightsaber Training
Rey's training - to be a Jedi or whatever other label they may put on it in future if she does indeed bring balance - goes up a notch here, as we get a scene of her swinging a lightsaber about.
We've already seen that she is rather proficient with a lightsaber, but then it was running on pure adrenaline, emotion, and instinct, against an injured opponent. Her technique could definitely do with a lot of refinement, and that's what we're seeing here, mirroring Luke's own early days of training back on the Millennium Falcon.
Also note that she's still using Luke's blue lightsaber, which means that after the powerful shot of her handing it to him, he then gives it back to her. That could just be for training purposes, may mean he still has his green lightsaber and is keeping that instead, or - and this one fits with the themes of this trailer - no longer wants to use such a weapon. Luke is Palpatine confirmed.
We also hear him say "it's so much bigger" which again fits with that notion, and of the Force being about more than Jedi and Sith.