I don't know a lot about this either, so I did a quick search that turned up some info at an immigration law firm's site. (Obviously it's not as authoritative as real research on fed immigration laws/regs, but it seems to provide a fair summary.) Here's how the law firm explains it:
Political Asylum
What is political asylum?
It is a special and exceptional immigration benefit that if granted leads to the permanent residency in the United States and is based on the applicant's ability to show that the applicant has a well founded fear of persecution in his/her country of origin on account of race, religion, nationality, membership in a particular social group or political opinion.
I. How do I qualify for asylum?
The Refugee Act of 1980, and subsequent modifications of it incorporated into the Immigration and Nationality Act, provides that:
Any alien who is physically present in the United States or who arrives in the United States ... irrespective of such alien's status, may apply for asylum ... (sec. 208 of the INA)
If you or anyone you know have been persecuted by the government of your country based on your race, ethnicity, social group, religion or political opinion and you are afraid to go back to your country because you will be arrested, tortured or killed you may qualify for political asylum in the U.S.
What is persecution?
Persecution is a severe form of discrimination, harassment, torture, or any other type of harm that's being committed against the asylum applicant by the government of his country directly or indirectly. Forced or irregular recruitment into the military, cruel practices rooted in culture or religion, military operations against certain groups of people, rape or sexual assault on account of race, ethnic origin, membership in social group, harm to family members are the examples of persecution that was in some cases found sufficient by the U.S. government to grant political asylum to persons subjected to these forms of persecution.
Past persecution and future persecution
The asylum applicant must prove to the U.S. government official /interviewing officer or immigration judge that the applicant was not only subjected to severe persecution by his/her government agents in the past, but is more likely than not to be persecuted again if the applicant is returned to his/her country.
Is it important who persecutes me?
Yes, the U.S. asylum law provides for protection from persecution by government agents of the foreign government - the asylum applicant must show that it was his /her government that persecuted the applicant.
http://www.dmitrylaw.com/attorney/immigration-lawyer-los-angeles/political-asylum.html