Lisa Wade of Sociological Images posted her comments on a recent Pew survey that explains why the "the majority of Americans are in favor of extending marriage to same-sex couples."
People offered a range of reasons for why they changed their minds. The most common response involved coming into contact with someone that they learned was homosexual. A third of respondents said that knowing a gay, lesbian, or bisexual person was influential in making them rethink their position on gay marriage. This is consistent with the Contact Hypothesis, the idea that (positive) experiences with someone we fear or dislike will result in changes of opinion.