I interpret that to mean she was shown a glimpse of her destiny.
She started out suppressing all desire to go out and do something, because she was kind of the opposite of Luke in that she wanted to stay where she was, despite knowing that it's important to actually make something of herself. Touching the lightsaber showed her that that's not what she was made for. She had to go and find Kylo, turn him to the light, etc.
She got a vision of what she was supposed to involve herself in, that being the Jedi, the past, and the legacy of the Skywalkers. She had to solve that mystery and set things right.
This was meant to be the moment that let her understand that she had to leave, because she would ponder that glimpse she got for a while until eventually getting pulled into it. It also shows the stubborn and naive side of her.
Also, it gave the audience a hint as to what happened with Kylo and Luke. The idea being that he killed the Jedi Order along with the Knights of Ren. Yes, that's not exactly how it happened in the comics, but that's just some subtle retroactive continuity for you. We can just assume the vision was metaphorical, since he did kill Jedi to please Ren.
Or it could just be Kylo leading the Knights of Ren to kill some random acolytes as they were prone to do. I don't know if that was always the intention, but that's what the Rise of Kylo Ren seems to support.
EDIT: TL;DR - It's the Force showing her that she needs to go and sort this whole Kylo conflict out and in the process tells the audience that Kylo killed the Jedi Order and has been going around killing more people. We learn why in the comics.