Apple may not have invented the smartphone...
But they pretty much set the mold by taking the existing technology and infrastructure of the iPod, adding a highly polished and well designed UI, and then integrating everything with network-agnostic functionality.
Back when the iPhone first launched, people were still thinking of smart phones as miniaturised computers - or at best, an upgraded PDA - and designed the UI and software accordingly. So, apps had scroll-bars which needed to be physically clicked and dragged with pixel-perfect precision, which was generally only feasible if you had a stylus or sharp fingernails. It' was all clunky and clumsy, especially since many devices still used single-touch resistive touch-screens and often sacrificed screen-size in favour of an awkwardly small physical keyboard.
Conversely, Apple ditched the physical keyboard and built the UI from the ground up to use capacitive multi-touch, with little bits of auto-assist technology built in everywhere. And to quote the old Apple Marketing slogan, It Just Worked - as long as you were happy with the functionality Apple was willing to give you.
Then too, Apple had some other advantages: the iPhone used the same connector as their iPod line. This meant that there was already a reasonably large third-party ecosystem out there (e.g. powered speakers, recharging docks) and the cost of buying replacement cables, etc was low. Also, you could share cables/battery packs/etc between your devices and you could charge via USB. And if you did want to use your iPhone for music, it had a 3.5mm headphone jack, unlike most other mobile phones at the time, which would at best have a 2.5mm jack for a mono earpiece
(And yes, there's an irony there, given that Apple has now ditched the 3.5mm jack. And to be fair, manufacturers like Nokia and Sony-Ericsson had fairly standardised power connectors, but these didn't transmit audio and they only sold cabled wall-warts, so if you did want to recharge via USB, you had to track down third-party cables, sometimes of highly dubious quality)
Finally, for all that iTunes is looking very long in the tooth these days, at the time, it was leagues ahead of the garbage supplied by other major manufacturers at the time (Sony, Nokia, etc), which were often unstable/buggy or hamstrung by politics. Sony in particular were bad for this, presumably because the media division ranked higher than the hardware division; the minidisk in particular was one technology which could have made a much bigger impact if they hadn't been locked it down so much to try and prevent music copying.
The use of iTunes also had a further impact, in that it provided a standardised and relatively simple way to push software updates to an iPhone, improving performance, stability and features. This was something other manufacturers simply couldn't begin to do, thanks in no small part to the fact that there was often network-specific elements embedded in the OS.
And iTunes also had a further, unexpected benefit, in that it offered a way for people to easily download - and pay for - new applications to their phone. Everything I've seen/read/remembered suggests that Apple initially failed to realise the significance of this, despite the fact that even basic games like Nokia's Snake had become a part of popular culture. Still, in time, iTune apps actually became a major driver of iPhone sales, thanks to effectively-exclusive titles such as Angry Birds, Fruit Ninja and Doodle Jump.
Mind you, for all that I admire and recognise the impacts of the iPhone, I've never actually owned one: they've always been too expensive, especially if you wanted extra storage and by the time I could justify buying one, Android phones were giving better bang for the buck, as well as offering far more flexibility - varied screen sizes, expandable storage, replacable batteries, widgets, etc.