Barack Obama served as a director on for a charitable fund called the Wood' s fund for Chicago from 1993 to 2002. Ayers served as a director for the same organzation from 1999 to 2008. The also served on a couple of six person discussion panels together in 1997 and 2002.
http://en.wikipedia.org/wiki/Bill_Ayers_2008_presidential_election_controversy
In a 2013 interview he had this to say regarding his relationship to Barack Obama.
"David Axelrod said we were friendly, that was true; we served on a couple of boards together, that was true; he held a fundraiser in our living room, that was true; Michelle [Obama] and Bernardine were at the law firm together, that was true. Hyde Park in Chicago is a tiny neighborhood, so when he said I was “a guy around the ighborhood,” that was true. Today, I wish I knew him better and he was listening to me. Obama’s not a radical. I wish he were, but he’s not.[67]
Bill Ayers was a co-founder of a terrorist organization called the Weather Underground which operated between 1969 and 1975 is still unapologetic about his actions.
Among there attacks include March of 1971 they bombed the U.S Capitol, in May of 1972 they bombed the Pentagon. In 1975 they bombed the U.S. State department building. This last attack they stated was because of the escalation of the Vietnam War which was already over. They also attempted to bomb the home of judge Murtah who said things unfavorable to their cause, while he, his wife and children were in the home. Bill Ayers denies his organization had anything to do with this but those who claim to belong the Weather Underground have said they were responsible. His former girlfriend was killed while trying to make a bomb intended to kill those attending a military dance. Bill Ayers says he is glad they were unsuccessful and it would have been a great trajedy. In 1981 two former members attempted to rob a brinks truck and murdered two policeman and a security gaurd in the process. Bill Ayers adopted their children while they went to prison. He claims he had nothing to do with those actions. Of the two former members, he says they are good people who did a terrible thing.
Former member turned FBI informant, Larry Grathwol, said that Ayers admitted that his wife, Bernadine Dohrn murdered 44 yearold San Francisco police officer Srgt. Mcdonald. Ayers denies this and said Grathwol was a paid liar.
In terms of political philosophy here is a quote from his 1974 book Prarie Fire
"We are a Guerilla organization. We are communist men and women unerground in the United States for more than four years."
"We need a revolutionary communist party struggle in order to lead the struggle, give coherence and direction to fight, sieze power and build the new society."
Bill Ayers continues to say that he does not regret his actions and wishes he had done more.
This is a quote from his wife, Bernadine Dohrn, that expresses her philosophy:
"We are building a communist organization to be part of the forces which build a revolutionary communist party to lead the working class to seize power and build socialism. [...] We must further the study of Marxism-Leninism within the WUO [Weather Underground Organization]. The struggle
for Marxism-Leninism is the most significant development in our recent history. [...] We discovered thru our own experiences what revolutionaries all over the world have found — that Marxism-Leninism is the science of revolution, the revolutionary ideology of the working class, our guide to the struggle [...]" According to a 1974 FBI study of the group, Dohrn's article signaled a developing commitment to Marxism-Leninism that had not been clear in the group's previous statements, despite their trips to Cuba and contact with Vietnamese communists there.[19
As recently as 2010, Bernadine Dohrn said that she still believes in violence as a way of achieving her goals.
He appeared on Fox News with Megan Kelly to talk about his past. He stated that he was not sorry for his actions,which he says only killed property and not people.
Any reasonable person would say Obama has hid the true relationship between himself and Ayers. However,a lot of people in those circles had a relationship with Ayers and he was widely accepted and respected in the academic world of Chicago. That being said, there is no way the news media would have let a republican get away with having such a tie to a questionable person like Ayers.