Battery life is easily the best thing about this phone for me. And I'm a super power user. I email and blog from my phone and run 10+ social media accounts from my phone. Plus I go to gym and watch Netflix for an hour then listen to music for another hour or so. Not to mention I stream music whenever I'm in my car. Or use the GPS.
Yesterday for example, I took phone off charger at around 10AM and at around 7PM the battery was at like 10 percent which I am totally fine with due to my heavy activity and usage.
I've been leaving phone unplugged all night while I sleep just to test things out and only see like a 5 percent droppage. Which is pretty solid for 8 hours approximately of it being unplugged. So if you were to times that by 3 {24 hours), the battery life could easily last a complete day with minimum usage. But for me, I consider a day to be 8 to 10 hours since usually within 8 hours id have access to a charger of some kind anyway if I needed a boost.
I think when Samsung said all day battery, they meant in the literal sense that it is in fact possible. But the majority of us will probably never actually reach that 24 hour threshold due to our usage and I'm fine with that.