In the past decade, support for gay marriage has been steadily on the rise.  According to a comprehensive report done by the Pew Research Center for the People and the Press, this steady increase has been defined by the generational gap, although all generations have seen increases in support for same-sex marriage.
The Millennial Generation (those born after 1980) has seen the most dramatic shift, rising from 51% favoring legalized same-sex marriages in 2003 to 70% in 2013.  In addition to the substantial increase, the Millennial Generation also makes up a larger percentage of the adult population now than it did in 2003 (tripling from 9% to 27%).

Millennials have not been alone in coming around to legalizing same-sex marriages.  The Silent Generation (1928-1945) has almost doubled its rate of support over the same span of ten years, increasing from 17% to 31%.  Baby Boomers (1946-1964) and Generation X (1965-1980) have seen more modest increases in support from 33% to 38% and 41% to 49%, respectively.

To deepen the understanding of shifting attitudes, surveyors asked respondents whether their views on same-sex marriage had changed or if it had always been that way.  One-in-seven (14%) of the entire population have changed their minds to support same-sex marriage (this accounts for 28% of all proponents of same-sex marriage).  The main reason for changing one's mind, according to respondents, was knowing someone who was homosexual (32%), while a close second was personally growing more open (25%).  Be sure to check out the rest of the report, which shows larger societal responses to homosexuality in general, shifting responses to gay rights issues,and changing religious stances.