The most reported uses are for checking email during programs and commercials. Interestingly, reported usage is fairly consistent near 60%, for both men and women, for tablet and smartphone owners, and whether during programs or commercials. Surfing for unrelated info and visiting social media sites are the next most reported, followed by checking sports scores. Use to look up information related to the program or commercial trailed was less common (about 30% for program info, and only 15-20% for ad-related information).While the report generally suggests that multitasking on mobile devices while watching TV is becoming more common and widespread, the fact that social media use and programming related use weren't nearly as common suggests the goal of developing a connected viewing experience and social TV still has a way to go.
Sources - What TV viewers are doing on their tablets, smartphones, Lost Remote.
Nielsen press release
edited - added link to earlier "social TV" post.