The Law of Chastity is essentially commandments from God to live a clean and moral life. In large part is about reserving sexual relations for marriage. There are great blessings that come from living a chaste life. 
 
Here are some better explanations: Law of Chastity answered

While the Core of the Law of Chastity is absolving from sexual relations till marriage it also covers dress and media.  
 
Modesty is a important part of Chastity all LDS members are strongly incouraged to wear modest dress, which means that the body is not revealed or displayed in a manner that would cause sexual arousal. Short skits, low cut pants or shirts, belly shirts, ect. This standard applies both to men and women.  
 
Also we are encouraged to refrain from all media that glories or encourages pre-marital sex. Whether it be music, television, movies, or pornography.  
 
We are also commanded to not have any type of contact with ourselves or another person that creates sexual pleasure of any kind.  
 
Lastly the Law of Chastity also prohibits any kind of homosexual relations.