In terms of demographics, age and usage are negatively related, with younger age groups being more likely to be "cell internet users." Having at least some college education is also related to use of cell phones for internet access, and income is also positively related to cell internet usage. Cell phone users living in rural areas were less likely to use their phones for internet access - while the survey didn't specify, at least some of this may be related to the lower cell data speeds in many rural areas.
There was, in addition, a small gender effect with men reporting higher usage (65%) than women (60%).
This survey also found meaningful differences between race/ethnic groups - with Blacks reporting the highest rate of adoption (74%), followed by Hispanics (68%), with Whites trailing at 59%. This pattern has been found fairly consistently in mobile device usage studies in the U.S., and is often attributed to the argument that the mobile devices often serve as the only (or the least expensive) Internet connection point available. (That is, more limited use of laptops and desktops connecting to wired Internet services in the home.)
While a third of cell internet users reported going online mostly through their phones, more than half (53%) have indicated that the phone was a secondary contact point, with another device serving as their primary online connection. And remember that more than a third of cell phone owners (37%) reported that they do not access the internet through their cell phones.
It gets more interesting when you look at race/ethnicity, income, and education. Along the lines of the argument that mobile devices may be the most viable internet access point for poor and minority users, White cell internet users had the lowest likelihood of reported their phones as their primary internet access point (27%). Interestingly, though, the level of cells as primary device was among Hispanics (at 60%), rather than Blacks (at 43%).
The relationship between usage of cell phones as primary internet connections with both education and income were negative, with lower income groups and those with no college being the most likely to report their cell phones as their primary internet connection. This would seem consistent with the idea that mobile devices can be a cheaper and more convenient way of accessing the net for the less advantaged.
Sources - Cell Internet Use 2013, Pew Research Center
Cell Internet Use 2013, full research report from Pew Research Center