Re: I sort of agree.
I don't think that any application is "killer" - different people have different reasons. For me, I love having maps everywhere, from the Google Maps app in ~2006, to Nokia's (and later Google's) free sat nav.
As much as I hate to admit it, sites like Facebook and Twitter probably helped a lot. Although social networks existed in the early 2000s, these were sites like Livejournal where people were expected to write a lot more, and it wasn't so easy to do on a phone - so even though having Internet everywhere might have been something useful, most websites don't work well on a phone. Email might have been useful, but most people were probably happy to use texts, and wait until they got home for email.
But the obsession with reading or writing short status updates wherever you are suddenly made Internet on phones much more useful.
Another point may be that Internet data allowances used to be far more stingy. I was someone who wanted Internet, but rarely used a phone, but you could only get Internet years ago buy paying for a high end contract where you were paying for loads of hours and texts, things that I didn't need. The moment it was allowed on PAYG made it much more viable for me.
Also, I don't think there was really any sudden event - if you look at sales, there's been continual growth in Internet enabled phones (which remember isn't just so-called "smart" phones). It's more that as devices become more powerful, the technology is more usable. And web browsing - one of the most useful things - is also one of the most power hungry for most users. Around 2000, you had the spec that made them comparable to earlier home computers, but not very good for browsing. By 2005, this was more plausible. By 2008, this was much more doable, though it still wasn't completely smooth, and opening loads of memory hungry tabs might be a problem. By 2010 onwards, it's mature.