Luke Skywalker acknowledged a darkness that Rey sensed under the island. Then
Rey went down there and it turned out to be a small cave, water, and a strange reflective wall.
What was so bad about this? What was "dark" about it? And what meaning was
behind the visions she saw of herself repeated in the past and future, and of her own face when she asked to see her parents?
Since the Force exists everywhere in the galaxy, it manifests in stronger concentrations in some places. Previous examples in canon include the cave on Dagobah:
That place... is strong with the dark side of the Force. A domain of evil it is. In you must go.
-Yoda, Empire Strikes Back
And Mustafar also (can't find a citation for that).
The same is true about the 'cave' on Ahch-To; that the dark side of the force is strong in that specific area. It doesn't mean that there's something that will harm or kill people who enter, just that dark force energy flows through that place.
As for Rey's specific visions, it's only conjecture at this point what they mean. Snoke could have been influencing them to draw Rey in, or it could be making Rey realize her parents don't matter, the Force is only concerned with her.
The film's Visual Dictionary strongly implies that the "mirror cave" is a actually an entirely natural phenomenon. The ancient Jedi felt that the island represented an ideal spot for their meditation on the nature of the Force, with the upper part of the island a natural confluence of light side energies and the underside a confluence of dark side energies.
"A natural convergence of energy, strong in the dark side of The Force, manifests itself on the eastern side of the island"
The implications were that it was the dark side. Shortly after this scene, we have Snoke and Kylo Ren conversing about her and noting that the dark side "can get her what she wants", implying it's down that hole.
What she wants is to know who her parents were
Out of universe, the scene is clearly directed at fans, who would recognize the infamous scene on Ahch-to as being where the dark side was. As to why the need for the scene, consider the setup
Luke has confirmed Kylo's version of events. That he, briefly, wanted to murder Ben Solo, and Ben used the opportunity to strike back. Because he didn't tell her the whole truth, Rey rebels against Luke, going to the "dark place" that was drawing her in her earlier vision. So she goes and finds the mirror wall.
It's obvious that she's being tempted by the dark side in some fashion, and it's heavily implied later that she actually got the answer she wanted. Kylo explicitly calls her on it, telling her he knows who her parents were, and that she "knows it's true", before spilling the beans.
It's never spelled out why she didn't turn, or if that event changed her alignment in any way. All we know is that, after meeting with Kylo Ren again, she rejects being a Sith.
