What was the ideal idea that they have, both of the ambitious guest and the family's member?
Both the family members and the guest wish for their ideals. The guest, the young man, wishes that he will accomplish great things in his life. So far, he has not reached his destiny, but he is young, and has hope that in the future, he will make something of himself. The more the discussion continues, the more the father and grandmother think about things that they, too, wish they had, or had done. Meanwhile, the storm outside is getting worse and worse.
The grandmother begins talking about her death, and that she wants her family to let her corpse look in a mirror when she dies so she can see herself -- strange things like this. Even though the family pretends to be calm and feel safe, the storm raging outside is a stark contrast to their illusion of safety. Finally, there is a huge rock slide, the people run outside, and are killed. If they had remained inside, they would have been saved because the house was not destroyed. None of them is saved and years later when people are looking at the ruins, there is no evidence of anyone - and they are not even sure whether or not there "may" have been a guest that night. So the young man goes into eternity in obscurity. A rather depressing story, huh?
There is a good discussion of this right here on eNotes.