Meaning?
I could ask you the same thing. The Snopes entry means just what it says. One of those quotes is not from Obama, others have been reworded or taken at least somewhat out of context. Still, quotes from the list are mostly but not entirely true.
Here is one of the incorrect Obama quotes: "I will stand with the Muslims should the political winds shift in an ugly direction."
I do not have a copy of The Audacity of Hope, but apparently Obama did not say that. According to several Internet sources, this is the actual quote from the book:
Of course, not all my conversations in immigrant communities follow this easy pattern. In the wake of 9/11, my meetings with Arab and Pakistani Americans, for example, have a more urgent quality, for the stories of detentions and FBI questioning and hard stares from neighbors have shaken their sense of security and belonging. They have been reminded that the history of immigration in this country has a dark underbelly; they need specific assurances that their citizenship really means something, that America has learned the right lessons from the Japanese internments during World War II, and that I will stand with them should the political winds shift in an ugly direction.
So the correct quote is "...I will stand with them should the political winds shift in a ugly direction." In context, "them" clearly refers not to Muslims in general or to Middle Eastern Muslims, but to presumably Muslim American citizens of Arab and Pakistani descent being threatened by other American citizens.
Context matters, and so do quotation marks.