In the For the Strength of the Youth, it goes over some things that have to do with what is acceptable, and what is not. What is acceptable dress for Sunday meetings, what is acceptable dating behavior, what is acceptable behavior and attitudes in general. This could be boiled down to what are the standards God has given us, with the follow up question of why it matters.
In Proverbs 10:32, it gives an argument that one way to define righteousness is by these standards of acceptableness:
32 The lips of the righteous know what is acceptable: but the mouth of the wicked speaketh frowardness.
and again in Romans 12:1-2, it makes this point even more clear:
1 I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service.
2 And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.
I heard a story about a girl who attended a fireside with the Prophet, and at the end of it she joined the other youth in line to meet him. When it was finally her turn, she held her program up against her chest to try and cover how low cut it was - because she felt embarrassed having the Prophet see her in something like that. We shouldn't base our decisions on trying to avoid being embarrassed, but it is something to keep in mind. Even if we can't give a direct reason or logical argument for the standards given us, I think that we all have the Light of Christ inside of us that can help us to feel what is right.
For a final word on trying to follow the standards, here is Mormon 7:44 on what following the standards can help us become:
44 If so, his faith and hope is vain, for none is acceptable before God, save the meek and lowly in heart; and if a man be meek and lowly in heart, and confesses by the power of the Holy Ghost that Jesus is the Christ, he must needs have charity; for if he have not charity he is nothing; wherefore he must needs have charity.