Since it's one thirty in the morning and since I feel like being 'that guy', I'll explain what this sequence is about for those who are lazy to look at the source link and since I don't know how to do the spoiler button on this site yet. Feel free to downvote me if you want.

What this sequence is showing is a theory that I feel some fans have come up with; What if they kept their scars from any Neutral or No Mercy/Genocide runs? What if the underground was haunted by the events of previous playthroughs? Undyne could have had two eyes prior to meeting the character and wore the patch cause it looked awesome to her. Over time though, she would wake up one day and found out that she actually loses it for reasons she doesn't know, same for what's happening to the others in the sequence. Yet it seems that Sans is the only one that knows what's going on with him and the rest.